A class of weakly compact sets in Lebesgue–Bochner spaces
Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, con...
Ausführliche Beschreibung
Autor*in: |
Rodríguez, José [verfasserIn] |
---|
Format: |
E-Artikel |
---|---|
Sprache: |
Englisch |
Erschienen: |
2017transfer abstract |
---|
Schlagwörter: |
---|
Umfang: |
13 |
---|
Übergeordnetes Werk: |
Enthalten in: Frequent mutations in the RPL22 gene and its clinical and functional implications - 2013, a journal devoted to general, geometric, set-theoretic and algebraic topology, Amsterdam [u.a.] |
---|---|
Übergeordnetes Werk: |
volume:222 ; year:2017 ; day:15 ; month:05 ; pages:16-28 ; extent:13 |
Links: |
---|
DOI / URN: |
10.1016/j.topol.2017.02.075 |
---|
Katalog-ID: |
ELV035730714 |
---|
LEADER | 01000caa a22002652 4500 | ||
---|---|---|---|
001 | ELV035730714 | ||
003 | DE-627 | ||
005 | 20230625205348.0 | ||
007 | cr uuu---uuuuu | ||
008 | 180603s2017 xx |||||o 00| ||eng c | ||
024 | 7 | |a 10.1016/j.topol.2017.02.075 |2 doi | |
028 | 5 | 2 | |a GBVA2017005000011.pica |
035 | |a (DE-627)ELV035730714 | ||
035 | |a (ELSEVIER)S0166-8641(17)30154-2 | ||
040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
041 | |a eng | ||
082 | 0 | |a 510 | |
082 | 0 | 4 | |a 510 |q DE-600 |
082 | 0 | 4 | |a 610 |q VZ |
082 | 0 | 4 | |a 610 |q VZ |
084 | |a 44.11 |2 bkl | ||
100 | 1 | |a Rodríguez, José |e verfasserin |4 aut | |
245 | 1 | 0 | |a A class of weakly compact sets in Lebesgue–Bochner spaces |
264 | 1 | |c 2017transfer abstract | |
300 | |a 13 | ||
336 | |a nicht spezifiziert |b zzz |2 rdacontent | ||
337 | |a nicht spezifiziert |b z |2 rdamedia | ||
338 | |a nicht spezifiziert |b zu |2 rdacarrier | ||
520 | |a Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . | ||
520 | |a Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . | ||
650 | 7 | |a 46G10 |2 Elsevier | |
650 | 7 | |a 46B50 |2 Elsevier | |
773 | 0 | 8 | |i Enthalten in |n Elsevier |t Frequent mutations in the RPL22 gene and its clinical and functional implications |d 2013 |d a journal devoted to general, geometric, set-theoretic and algebraic topology |g Amsterdam [u.a.] |w (DE-627)ELV011305770 |
773 | 1 | 8 | |g volume:222 |g year:2017 |g day:15 |g month:05 |g pages:16-28 |g extent:13 |
856 | 4 | 0 | |u https://doi.org/10.1016/j.topol.2017.02.075 |3 Volltext |
912 | |a GBV_USEFLAG_U | ||
912 | |a GBV_ELV | ||
912 | |a SYSFLAG_U | ||
912 | |a SSG-OLC-PHA | ||
912 | |a GBV_ILN_22 | ||
912 | |a GBV_ILN_40 | ||
912 | |a GBV_ILN_62 | ||
912 | |a GBV_ILN_73 | ||
912 | |a GBV_ILN_252 | ||
936 | b | k | |a 44.11 |j Präventivmedizin |q VZ |
951 | |a AR | ||
952 | |d 222 |j 2017 |b 15 |c 0515 |h 16-28 |g 13 | ||
953 | |2 045F |a 510 |
author_variant |
j r jr |
---|---|
matchkey_str |
rodrguezjos:2017----:casfekyopcstilbsub |
hierarchy_sort_str |
2017transfer abstract |
bklnumber |
44.11 |
publishDate |
2017 |
allfields |
10.1016/j.topol.2017.02.075 doi GBVA2017005000011.pica (DE-627)ELV035730714 (ELSEVIER)S0166-8641(17)30154-2 DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 610 VZ 44.11 bkl Rodríguez, José verfasserin aut A class of weakly compact sets in Lebesgue–Bochner spaces 2017transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . 46G10 Elsevier 46B50 Elsevier Enthalten in Elsevier Frequent mutations in the RPL22 gene and its clinical and functional implications 2013 a journal devoted to general, geometric, set-theoretic and algebraic topology Amsterdam [u.a.] (DE-627)ELV011305770 volume:222 year:2017 day:15 month:05 pages:16-28 extent:13 https://doi.org/10.1016/j.topol.2017.02.075 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_22 GBV_ILN_40 GBV_ILN_62 GBV_ILN_73 GBV_ILN_252 44.11 Präventivmedizin VZ AR 222 2017 15 0515 16-28 13 045F 510 |
spelling |
10.1016/j.topol.2017.02.075 doi GBVA2017005000011.pica (DE-627)ELV035730714 (ELSEVIER)S0166-8641(17)30154-2 DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 610 VZ 44.11 bkl Rodríguez, José verfasserin aut A class of weakly compact sets in Lebesgue–Bochner spaces 2017transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . 46G10 Elsevier 46B50 Elsevier Enthalten in Elsevier Frequent mutations in the RPL22 gene and its clinical and functional implications 2013 a journal devoted to general, geometric, set-theoretic and algebraic topology Amsterdam [u.a.] (DE-627)ELV011305770 volume:222 year:2017 day:15 month:05 pages:16-28 extent:13 https://doi.org/10.1016/j.topol.2017.02.075 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_22 GBV_ILN_40 GBV_ILN_62 GBV_ILN_73 GBV_ILN_252 44.11 Präventivmedizin VZ AR 222 2017 15 0515 16-28 13 045F 510 |
allfields_unstemmed |
10.1016/j.topol.2017.02.075 doi GBVA2017005000011.pica (DE-627)ELV035730714 (ELSEVIER)S0166-8641(17)30154-2 DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 610 VZ 44.11 bkl Rodríguez, José verfasserin aut A class of weakly compact sets in Lebesgue–Bochner spaces 2017transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . 46G10 Elsevier 46B50 Elsevier Enthalten in Elsevier Frequent mutations in the RPL22 gene and its clinical and functional implications 2013 a journal devoted to general, geometric, set-theoretic and algebraic topology Amsterdam [u.a.] (DE-627)ELV011305770 volume:222 year:2017 day:15 month:05 pages:16-28 extent:13 https://doi.org/10.1016/j.topol.2017.02.075 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_22 GBV_ILN_40 GBV_ILN_62 GBV_ILN_73 GBV_ILN_252 44.11 Präventivmedizin VZ AR 222 2017 15 0515 16-28 13 045F 510 |
allfieldsGer |
10.1016/j.topol.2017.02.075 doi GBVA2017005000011.pica (DE-627)ELV035730714 (ELSEVIER)S0166-8641(17)30154-2 DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 610 VZ 44.11 bkl Rodríguez, José verfasserin aut A class of weakly compact sets in Lebesgue–Bochner spaces 2017transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . 46G10 Elsevier 46B50 Elsevier Enthalten in Elsevier Frequent mutations in the RPL22 gene and its clinical and functional implications 2013 a journal devoted to general, geometric, set-theoretic and algebraic topology Amsterdam [u.a.] (DE-627)ELV011305770 volume:222 year:2017 day:15 month:05 pages:16-28 extent:13 https://doi.org/10.1016/j.topol.2017.02.075 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_22 GBV_ILN_40 GBV_ILN_62 GBV_ILN_73 GBV_ILN_252 44.11 Präventivmedizin VZ AR 222 2017 15 0515 16-28 13 045F 510 |
allfieldsSound |
10.1016/j.topol.2017.02.075 doi GBVA2017005000011.pica (DE-627)ELV035730714 (ELSEVIER)S0166-8641(17)30154-2 DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 610 VZ 44.11 bkl Rodríguez, José verfasserin aut A class of weakly compact sets in Lebesgue–Bochner spaces 2017transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . 46G10 Elsevier 46B50 Elsevier Enthalten in Elsevier Frequent mutations in the RPL22 gene and its clinical and functional implications 2013 a journal devoted to general, geometric, set-theoretic and algebraic topology Amsterdam [u.a.] (DE-627)ELV011305770 volume:222 year:2017 day:15 month:05 pages:16-28 extent:13 https://doi.org/10.1016/j.topol.2017.02.075 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_22 GBV_ILN_40 GBV_ILN_62 GBV_ILN_73 GBV_ILN_252 44.11 Präventivmedizin VZ AR 222 2017 15 0515 16-28 13 045F 510 |
language |
English |
source |
Enthalten in Frequent mutations in the RPL22 gene and its clinical and functional implications Amsterdam [u.a.] volume:222 year:2017 day:15 month:05 pages:16-28 extent:13 |
sourceStr |
Enthalten in Frequent mutations in the RPL22 gene and its clinical and functional implications Amsterdam [u.a.] volume:222 year:2017 day:15 month:05 pages:16-28 extent:13 |
format_phy_str_mv |
Article |
bklname |
Präventivmedizin |
institution |
findex.gbv.de |
topic_facet |
46G10 46B50 |
dewey-raw |
510 |
isfreeaccess_bool |
false |
container_title |
Frequent mutations in the RPL22 gene and its clinical and functional implications |
authorswithroles_txt_mv |
Rodríguez, José @@aut@@ |
publishDateDaySort_date |
2017-01-15T00:00:00Z |
hierarchy_top_id |
ELV011305770 |
dewey-sort |
3510 |
id |
ELV035730714 |
language_de |
englisch |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV035730714</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230625205348.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">180603s2017 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.topol.2017.02.075</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">GBVA2017005000011.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV035730714</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0166-8641(17)30154-2</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">610</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">610</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44.11</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rodríguez, José</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A class of weakly compact sets in Lebesgue–Bochner spaces</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017transfer abstract</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">13</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] .</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] .</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">46G10</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">46B50</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier</subfield><subfield code="t">Frequent mutations in the RPL22 gene and its clinical and functional implications</subfield><subfield code="d">2013</subfield><subfield code="d">a journal devoted to general, geometric, set-theoretic and algebraic topology</subfield><subfield code="g">Amsterdam [u.a.]</subfield><subfield code="w">(DE-627)ELV011305770</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:222</subfield><subfield code="g">year:2017</subfield><subfield code="g">day:15</subfield><subfield code="g">month:05</subfield><subfield code="g">pages:16-28</subfield><subfield code="g">extent:13</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.topol.2017.02.075</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_252</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">44.11</subfield><subfield code="j">Präventivmedizin</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">222</subfield><subfield code="j">2017</subfield><subfield code="b">15</subfield><subfield code="c">0515</subfield><subfield code="h">16-28</subfield><subfield code="g">13</subfield></datafield><datafield tag="953" ind1=" " ind2=" "><subfield code="2">045F</subfield><subfield code="a">510</subfield></datafield></record></collection>
|
author |
Rodríguez, José |
spellingShingle |
Rodríguez, José ddc 510 ddc 610 bkl 44.11 Elsevier 46G10 Elsevier 46B50 A class of weakly compact sets in Lebesgue–Bochner spaces |
authorStr |
Rodríguez, José |
ppnlink_with_tag_str_mv |
@@773@@(DE-627)ELV011305770 |
format |
electronic Article |
dewey-ones |
510 - Mathematics 610 - Medicine & health |
delete_txt_mv |
keep |
author_role |
aut |
collection |
elsevier |
remote_str |
true |
illustrated |
Not Illustrated |
topic_title |
510 510 DE-600 610 VZ 44.11 bkl A class of weakly compact sets in Lebesgue–Bochner spaces 46G10 Elsevier 46B50 Elsevier |
topic |
ddc 510 ddc 610 bkl 44.11 Elsevier 46G10 Elsevier 46B50 |
topic_unstemmed |
ddc 510 ddc 610 bkl 44.11 Elsevier 46G10 Elsevier 46B50 |
topic_browse |
ddc 510 ddc 610 bkl 44.11 Elsevier 46G10 Elsevier 46B50 |
format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
format_main_str_mv |
Text Zeitschrift/Artikel |
carriertype_str_mv |
zu |
hierarchy_parent_title |
Frequent mutations in the RPL22 gene and its clinical and functional implications |
hierarchy_parent_id |
ELV011305770 |
dewey-tens |
510 - Mathematics 610 - Medicine & health |
hierarchy_top_title |
Frequent mutations in the RPL22 gene and its clinical and functional implications |
isfreeaccess_txt |
false |
familylinks_str_mv |
(DE-627)ELV011305770 |
title |
A class of weakly compact sets in Lebesgue–Bochner spaces |
ctrlnum |
(DE-627)ELV035730714 (ELSEVIER)S0166-8641(17)30154-2 |
title_full |
A class of weakly compact sets in Lebesgue–Bochner spaces |
author_sort |
Rodríguez, José |
journal |
Frequent mutations in the RPL22 gene and its clinical and functional implications |
journalStr |
Frequent mutations in the RPL22 gene and its clinical and functional implications |
lang_code |
eng |
isOA_bool |
false |
dewey-hundreds |
500 - Science 600 - Technology |
recordtype |
marc |
publishDateSort |
2017 |
contenttype_str_mv |
zzz |
container_start_page |
16 |
author_browse |
Rodríguez, José |
container_volume |
222 |
physical |
13 |
class |
510 510 DE-600 610 VZ 44.11 bkl |
format_se |
Elektronische Aufsätze |
author-letter |
Rodríguez, José |
doi_str_mv |
10.1016/j.topol.2017.02.075 |
dewey-full |
510 610 |
title_sort |
a class of weakly compact sets in lebesgue–bochner spaces |
title_auth |
A class of weakly compact sets in Lebesgue–Bochner spaces |
abstract |
Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . |
abstractGer |
Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . |
abstract_unstemmed |
Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] . |
collection_details |
GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_22 GBV_ILN_40 GBV_ILN_62 GBV_ILN_73 GBV_ILN_252 |
title_short |
A class of weakly compact sets in Lebesgue–Bochner spaces |
url |
https://doi.org/10.1016/j.topol.2017.02.075 |
remote_bool |
true |
ppnlink |
ELV011305770 |
mediatype_str_mv |
z |
isOA_txt |
false |
hochschulschrift_bool |
false |
doi_str |
10.1016/j.topol.2017.02.075 |
up_date |
2024-07-06T18:19:30.431Z |
_version_ |
1803854776035704832 |
fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV035730714</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230625205348.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">180603s2017 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.topol.2017.02.075</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">GBVA2017005000011.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV035730714</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0166-8641(17)30154-2</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">610</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">610</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44.11</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rodríguez, José</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A class of weakly compact sets in Lebesgue–Bochner spaces</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017transfer abstract</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">13</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] .</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Let X be a Banach space and μ a probability measure. A set K ⊆ L 1 ( μ , X ) is said to be a δ S -set if it is uniformly integrable and for every δ > 0 there is a weakly compact set W ⊆ X such that μ ( f − 1 ( W ) ) ≥ 1 − δ for every f ∈ K . This is a sufficient, but in general non-necessary, condition for relative weak compactness in L 1 ( μ , X ) . We say that X has property ( δ S μ ) if every relatively weakly compact subset of L 1 ( μ , X ) is a δ S -set. In this paper we study δ S -sets and Banach spaces having property ( δ S μ ). We show that testing on uniformly bounded sets is enough to check this property. New examples of spaces having property ( δ S μ ) are provided. Special attention is paid to the relationship with strongly weakly compactly generated (SWCG) spaces. In particular, we show an example of a SWCG (in fact, separable Schur) space failing property ( δ S μ ) when μ is the Lebesgue measure on [ 0 , 1 ] .</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">46G10</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">46B50</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier</subfield><subfield code="t">Frequent mutations in the RPL22 gene and its clinical and functional implications</subfield><subfield code="d">2013</subfield><subfield code="d">a journal devoted to general, geometric, set-theoretic and algebraic topology</subfield><subfield code="g">Amsterdam [u.a.]</subfield><subfield code="w">(DE-627)ELV011305770</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:222</subfield><subfield code="g">year:2017</subfield><subfield code="g">day:15</subfield><subfield code="g">month:05</subfield><subfield code="g">pages:16-28</subfield><subfield code="g">extent:13</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.topol.2017.02.075</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_252</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">44.11</subfield><subfield code="j">Präventivmedizin</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">222</subfield><subfield code="j">2017</subfield><subfield code="b">15</subfield><subfield code="c">0515</subfield><subfield code="h">16-28</subfield><subfield code="g">13</subfield></datafield><datafield tag="953" ind1=" " ind2=" "><subfield code="2">045F</subfield><subfield code="a">510</subfield></datafield></record></collection>
|
score |
7.399088 |