Order Continuous Probabilistic Riesz Norms

Abstract The concepts of order continuous norm, σ-order continuous norm, and Fatou norm defined on ordinary normed Riesz spaces are very important in the study of Riesz spaces. In this paper, we introduce the probabilistic analogues of such norms on a topological probabilistic normed Riesz (TPNR) sp...
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Autor*in:	Şençimen, Celaleddin [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	Topological probabilistic normed Riesz space Order continuous probabilistic Riesz norm -order continuous probabilistic Riesz norm Probabilistic Fatou norm

Übergeordnetes Werk:	Enthalten in: Vietnam journal of mathematics - Singapore : Springer, 1999, 44(2015), 2 vom: 31. Mai, Seite 295-305
Übergeordnetes Werk:	volume:44 ; year:2015 ; number:2 ; day:31 ; month:05 ; pages:295-305

Links:	Volltext

DOI / URN:	10.1007/s10013-015-0152-0

Katalog-ID:	SPR008016097

Internformat


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520			\|a Abstract The concepts of order continuous norm, σ-order continuous norm, and Fatou norm defined on ordinary normed Riesz spaces are very important in the study of Riesz spaces. In this paper, we introduce the probabilistic analogues of such norms on a topological probabilistic normed Riesz (TPNR) space, and investigate their basic properties. In this context, some well-known theorems of the classical theory of topological Riesz spaces are proved in the setting of TPNR spaces, but now using the tools of probabilistic normed (PN) spaces. However, an interesting and different point here is that, although the classical order continuous Riesz norms are order preserving, the probabilistic Riesz norms considered in this work are order reversing mappings due to the nature of probabilistic distances.
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650		4	\|a Order continuous probabilistic Riesz norm \|7 (dpeaa)DE-He213
650		4	\|a -order continuous probabilistic Riesz norm \|7 (dpeaa)DE-He213
650		4	\|a Probabilistic Fatou norm \|7 (dpeaa)DE-He213
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912			\|a GBV_ILN_31
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912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2018
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
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Indexfelder

author_variant	c ş cş
matchkey_str	article:23052228:2015----::recniuupoaiit
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publishDate	2015
allfields	10.1007/s10013-015-0152-0 doi (DE-627)SPR008016097 (SPR)s10013-015-0152-0-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Şençimen, Celaleddin verfasserin aut Order Continuous Probabilistic Riesz Norms 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The concepts of order continuous norm, σ-order continuous norm, and Fatou norm defined on ordinary normed Riesz spaces are very important in the study of Riesz spaces. In this paper, we introduce the probabilistic analogues of such norms on a topological probabilistic normed Riesz (TPNR) space, and investigate their basic properties. In this context, some well-known theorems of the classical theory of topological Riesz spaces are proved in the setting of TPNR spaces, but now using the tools of probabilistic normed (PN) spaces. However, an interesting and different point here is that, although the classical order continuous Riesz norms are order preserving, the probabilistic Riesz norms considered in this work are order reversing mappings due to the nature of probabilistic distances. Topological probabilistic normed Riesz space (dpeaa)DE-He213 Order continuous probabilistic Riesz norm (dpeaa)DE-He213 -order continuous probabilistic Riesz norm (dpeaa)DE-He213 Probabilistic Fatou norm (dpeaa)DE-He213 Enthalten in Vietnam journal of mathematics Singapore : Springer, 1999 44(2015), 2 vom: 31. Mai, Seite 295-305 (DE-627)300183968 (DE-600)1481450-X 2305-2228 nnns volume:44 year:2015 number:2 day:31 month:05 pages:295-305 https://dx.doi.org/10.1007/s10013-015-0152-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 44 2015 2 31 05 295-305
spelling	10.1007/s10013-015-0152-0 doi (DE-627)SPR008016097 (SPR)s10013-015-0152-0-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Şençimen, Celaleddin verfasserin aut Order Continuous Probabilistic Riesz Norms 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The concepts of order continuous norm, σ-order continuous norm, and Fatou norm defined on ordinary normed Riesz spaces are very important in the study of Riesz spaces. In this paper, we introduce the probabilistic analogues of such norms on a topological probabilistic normed Riesz (TPNR) space, and investigate their basic properties. In this context, some well-known theorems of the classical theory of topological Riesz spaces are proved in the setting of TPNR spaces, but now using the tools of probabilistic normed (PN) spaces. However, an interesting and different point here is that, although the classical order continuous Riesz norms are order preserving, the probabilistic Riesz norms considered in this work are order reversing mappings due to the nature of probabilistic distances. Topological probabilistic normed Riesz space (dpeaa)DE-He213 Order continuous probabilistic Riesz norm (dpeaa)DE-He213 -order continuous probabilistic Riesz norm (dpeaa)DE-He213 Probabilistic Fatou norm (dpeaa)DE-He213 Enthalten in Vietnam journal of mathematics Singapore : Springer, 1999 44(2015), 2 vom: 31. Mai, Seite 295-305 (DE-627)300183968 (DE-600)1481450-X 2305-2228 nnns volume:44 year:2015 number:2 day:31 month:05 pages:295-305 https://dx.doi.org/10.1007/s10013-015-0152-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 44 2015 2 31 05 295-305
allfields_unstemmed	10.1007/s10013-015-0152-0 doi (DE-627)SPR008016097 (SPR)s10013-015-0152-0-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Şençimen, Celaleddin verfasserin aut Order Continuous Probabilistic Riesz Norms 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The concepts of order continuous norm, σ-order continuous norm, and Fatou norm defined on ordinary normed Riesz spaces are very important in the study of Riesz spaces. In this paper, we introduce the probabilistic analogues of such norms on a topological probabilistic normed Riesz (TPNR) space, and investigate their basic properties. In this context, some well-known theorems of the classical theory of topological Riesz spaces are proved in the setting of TPNR spaces, but now using the tools of probabilistic normed (PN) spaces. However, an interesting and different point here is that, although the classical order continuous Riesz norms are order preserving, the probabilistic Riesz norms considered in this work are order reversing mappings due to the nature of probabilistic distances. Topological probabilistic normed Riesz space (dpeaa)DE-He213 Order continuous probabilistic Riesz norm (dpeaa)DE-He213 -order continuous probabilistic Riesz norm (dpeaa)DE-He213 Probabilistic Fatou norm (dpeaa)DE-He213 Enthalten in Vietnam journal of mathematics Singapore : Springer, 1999 44(2015), 2 vom: 31. Mai, Seite 295-305 (DE-627)300183968 (DE-600)1481450-X 2305-2228 nnns volume:44 year:2015 number:2 day:31 month:05 pages:295-305 https://dx.doi.org/10.1007/s10013-015-0152-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 44 2015 2 31 05 295-305
allfieldsGer	10.1007/s10013-015-0152-0 doi (DE-627)SPR008016097 (SPR)s10013-015-0152-0-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Şençimen, Celaleddin verfasserin aut Order Continuous Probabilistic Riesz Norms 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The concepts of order continuous norm, σ-order continuous norm, and Fatou norm defined on ordinary normed Riesz spaces are very important in the study of Riesz spaces. In this paper, we introduce the probabilistic analogues of such norms on a topological probabilistic normed Riesz (TPNR) space, and investigate their basic properties. In this context, some well-known theorems of the classical theory of topological Riesz spaces are proved in the setting of TPNR spaces, but now using the tools of probabilistic normed (PN) spaces. However, an interesting and different point here is that, although the classical order continuous Riesz norms are order preserving, the probabilistic Riesz norms considered in this work are order reversing mappings due to the nature of probabilistic distances. Topological probabilistic normed Riesz space (dpeaa)DE-He213 Order continuous probabilistic Riesz norm (dpeaa)DE-He213 -order continuous probabilistic Riesz norm (dpeaa)DE-He213 Probabilistic Fatou norm (dpeaa)DE-He213 Enthalten in Vietnam journal of mathematics Singapore : Springer, 1999 44(2015), 2 vom: 31. Mai, Seite 295-305 (DE-627)300183968 (DE-600)1481450-X 2305-2228 nnns volume:44 year:2015 number:2 day:31 month:05 pages:295-305 https://dx.doi.org/10.1007/s10013-015-0152-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 44 2015 2 31 05 295-305
allfieldsSound	10.1007/s10013-015-0152-0 doi (DE-627)SPR008016097 (SPR)s10013-015-0152-0-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Şençimen, Celaleddin verfasserin aut Order Continuous Probabilistic Riesz Norms 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The concepts of order continuous norm, σ-order continuous norm, and Fatou norm defined on ordinary normed Riesz spaces are very important in the study of Riesz spaces. In this paper, we introduce the probabilistic analogues of such norms on a topological probabilistic normed Riesz (TPNR) space, and investigate their basic properties. In this context, some well-known theorems of the classical theory of topological Riesz spaces are proved in the setting of TPNR spaces, but now using the tools of probabilistic normed (PN) spaces. However, an interesting and different point here is that, although the classical order continuous Riesz norms are order preserving, the probabilistic Riesz norms considered in this work are order reversing mappings due to the nature of probabilistic distances. Topological probabilistic normed Riesz space (dpeaa)DE-He213 Order continuous probabilistic Riesz norm (dpeaa)DE-He213 -order continuous probabilistic Riesz norm (dpeaa)DE-He213 Probabilistic Fatou norm (dpeaa)DE-He213 Enthalten in Vietnam journal of mathematics Singapore : Springer, 1999 44(2015), 2 vom: 31. Mai, Seite 295-305 (DE-627)300183968 (DE-600)1481450-X 2305-2228 nnns volume:44 year:2015 number:2 day:31 month:05 pages:295-305 https://dx.doi.org/10.1007/s10013-015-0152-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 44 2015 2 31 05 295-305
language	English
source	Enthalten in Vietnam journal of mathematics 44(2015), 2 vom: 31. Mai, Seite 295-305 volume:44 year:2015 number:2 day:31 month:05 pages:295-305
sourceStr	Enthalten in Vietnam journal of mathematics 44(2015), 2 vom: 31. Mai, Seite 295-305 volume:44 year:2015 number:2 day:31 month:05 pages:295-305
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Topological probabilistic normed Riesz space Order continuous probabilistic Riesz norm -order continuous probabilistic Riesz norm Probabilistic Fatou norm
dewey-raw	510
isfreeaccess_bool	false
container_title	Vietnam journal of mathematics
authorswithroles_txt_mv	Şençimen, Celaleddin @@aut@@
publishDateDaySort_date	2015-05-31T00:00:00Z
hierarchy_top_id	300183968
dewey-sort	3510
id	SPR008016097
language_de	englisch
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author	Şençimen, Celaleddin
spellingShingle	Şençimen, Celaleddin ddc 510 bkl 31.00 misc Topological probabilistic normed Riesz space misc Order continuous probabilistic Riesz norm misc -order continuous probabilistic Riesz norm misc Probabilistic Fatou norm Order Continuous Probabilistic Riesz Norms
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topic_title	510 ASE 31.00 bkl Order Continuous Probabilistic Riesz Norms Topological probabilistic normed Riesz space (dpeaa)DE-He213 Order continuous probabilistic Riesz norm (dpeaa)DE-He213 -order continuous probabilistic Riesz norm (dpeaa)DE-He213 Probabilistic Fatou norm (dpeaa)DE-He213
topic	ddc 510 bkl 31.00 misc Topological probabilistic normed Riesz space misc Order continuous probabilistic Riesz norm misc -order continuous probabilistic Riesz norm misc Probabilistic Fatou norm
topic_unstemmed	ddc 510 bkl 31.00 misc Topological probabilistic normed Riesz space misc Order continuous probabilistic Riesz norm misc -order continuous probabilistic Riesz norm misc Probabilistic Fatou norm
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title	Order Continuous Probabilistic Riesz Norms
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title_full	Order Continuous Probabilistic Riesz Norms
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title_sort	order continuous probabilistic riesz norms
title_auth	Order Continuous Probabilistic Riesz Norms
abstract	Abstract The concepts of order continuous norm, σ-order continuous norm, and Fatou norm defined on ordinary normed Riesz spaces are very important in the study of Riesz spaces. In this paper, we introduce the probabilistic analogues of such norms on a topological probabilistic normed Riesz (TPNR) space, and investigate their basic properties. In this context, some well-known theorems of the classical theory of topological Riesz spaces are proved in the setting of TPNR spaces, but now using the tools of probabilistic normed (PN) spaces. However, an interesting and different point here is that, although the classical order continuous Riesz norms are order preserving, the probabilistic Riesz norms considered in this work are order reversing mappings due to the nature of probabilistic distances.
abstractGer	Abstract The concepts of order continuous norm, σ-order continuous norm, and Fatou norm defined on ordinary normed Riesz spaces are very important in the study of Riesz spaces. In this paper, we introduce the probabilistic analogues of such norms on a topological probabilistic normed Riesz (TPNR) space, and investigate their basic properties. In this context, some well-known theorems of the classical theory of topological Riesz spaces are proved in the setting of TPNR spaces, but now using the tools of probabilistic normed (PN) spaces. However, an interesting and different point here is that, although the classical order continuous Riesz norms are order preserving, the probabilistic Riesz norms considered in this work are order reversing mappings due to the nature of probabilistic distances.
abstract_unstemmed	Abstract The concepts of order continuous norm, σ-order continuous norm, and Fatou norm defined on ordinary normed Riesz spaces are very important in the study of Riesz spaces. In this paper, we introduce the probabilistic analogues of such norms on a topological probabilistic normed Riesz (TPNR) space, and investigate their basic properties. In this context, some well-known theorems of the classical theory of topological Riesz spaces are proved in the setting of TPNR spaces, but now using the tools of probabilistic normed (PN) spaces. However, an interesting and different point here is that, although the classical order continuous Riesz norms are order preserving, the probabilistic Riesz norms considered in this work are order reversing mappings due to the nature of probabilistic distances.
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title_short	Order Continuous Probabilistic Riesz Norms
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up_date	2024-07-03T16:46:50.680Z
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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">SPR008016097</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220110200549.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2015 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10013-015-0152-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR008016097</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10013-015-0152-0-e</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="4"><subfield code="a">510</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Şençimen, Celaleddin</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Order Continuous Probabilistic Riesz Norms</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The concepts of order continuous norm, σ-order continuous norm, and Fatou norm defined on ordinary normed Riesz spaces are very important in the study of Riesz spaces. In this paper, we introduce the probabilistic analogues of such norms on a topological probabilistic normed Riesz (TPNR) space, and investigate their basic properties. In this context, some well-known theorems of the classical theory of topological Riesz spaces are proved in the setting of TPNR spaces, but now using the tools of probabilistic normed (PN) spaces. However, an interesting and different point here is that, although the classical order continuous Riesz norms are order preserving, the probabilistic Riesz norms considered in this work are order reversing mappings due to the nature of probabilistic distances.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topological probabilistic normed Riesz space</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Order continuous probabilistic Riesz norm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-order continuous probabilistic Riesz norm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probabilistic Fatou norm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Vietnam journal of mathematics</subfield><subfield code="d">Singapore : Springer, 1999</subfield><subfield code="g">44(2015), 2 vom: 31. 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