Measure, Integration & Real Analysis
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course,...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Axler, Sheldon [verfasserIn] |
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| Format: |
E-Book |
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| Sprache: |
Englisch |
| Erschienen: |
Cham: Springer Nature ; 2020 |
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| Rechteinformationen: |
Open Access All rights reserved |
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| Schlagwörter: |
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| Umfang: |
1 Online-Ressource (411 p.) |
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| Reihe: |
Graduate Texts in Mathematics |
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| Links: | |
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| ISBN: |
978-3-030-33143-6 |
| Katalog-ID: |
1836388330 |
|---|
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| 520 | |a This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online | ||
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9783030331436 978-3-030-33143-6 978 (DE-627)1836388330 (DE-599)KEP062109251 (OCoLC)1371338231 (OAPEN)23111 (EBP)062109251 DE-627 eng DE-627 rda eng PBKL bicssc Axler, Sheldon verfasserin aut Measure, Integration & Real Analysis Cham Springer Nature 2020 1 Online-Ressource (411 p.) Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Graduate Texts in Mathematics Open Access Unrestricted online access star This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online All rights reserved English Integral calculus & equations Integral calculus and equations https://library.oapen.org/bitstream/id/ce19d94d-b8b6-420f-9e69-d9f565703c26/1007045.pdf X:OAPEN Verlag OAPEN Library: download the publication kostenfrei http://library.oapen.org/handle/20.500.12657/23111 X:OAPEN Verlag OAPEN Library: description of the publication kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280043752 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280599211 OLR-OAPEN f z 01-03-23 30 01 0104 4280958688 GBV-OAPEN z 01-03-23 31 01 0027 4280234000 z 01-03-23 34 01 3551 427879777X OLR-OAPEN zi002 01-03-23 39 01 0547 4281149457 GBV-OAPEN ke 01-03-23 40 01 0007 4279866279 OLR-OAPEN xsn 01-03-23 63 01 3401 4281529292 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281751033 OLR-OAPEN z 01-03-23 70 01 0089 4280420300 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278616511 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343142787 OLR-OAL Vervielfältigungen (z.B. 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9783030331436 978-3-030-33143-6 978 (DE-627)1836388330 (DE-599)KEP062109251 (OCoLC)1371338231 (OAPEN)23111 (EBP)062109251 DE-627 eng DE-627 rda eng PBKL bicssc Axler, Sheldon verfasserin aut Measure, Integration & Real Analysis Cham Springer Nature 2020 1 Online-Ressource (411 p.) Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Graduate Texts in Mathematics Open Access Unrestricted online access star This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online All rights reserved English Integral calculus & equations Integral calculus and equations https://library.oapen.org/bitstream/id/ce19d94d-b8b6-420f-9e69-d9f565703c26/1007045.pdf X:OAPEN Verlag OAPEN Library: download the publication kostenfrei http://library.oapen.org/handle/20.500.12657/23111 X:OAPEN Verlag OAPEN Library: description of the publication kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280043752 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280599211 OLR-OAPEN f z 01-03-23 30 01 0104 4280958688 GBV-OAPEN z 01-03-23 31 01 0027 4280234000 z 01-03-23 34 01 3551 427879777X OLR-OAPEN zi002 01-03-23 39 01 0547 4281149457 GBV-OAPEN ke 01-03-23 40 01 0007 4279866279 OLR-OAPEN xsn 01-03-23 63 01 3401 4281529292 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281751033 OLR-OAPEN z 01-03-23 70 01 0089 4280420300 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278616511 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343142787 OLR-OAL Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 24-06-23 110 01 3110 4281334165 OLR-GBV-OAPEN Open Access z 01-03-23 136 01 3526 4279507341 OLR-OAPEN z 01-03-23 147 01 3528 4281976140 OLR-OAPEN frei verfügbar für Europa-Universität Flensburg, Hochschule Flensburg und Zentrale Hochschulbibliothek Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. 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9783030331436 978-3-030-33143-6 978 (DE-627)1836388330 (DE-599)KEP062109251 (OCoLC)1371338231 (OAPEN)23111 (EBP)062109251 DE-627 eng DE-627 rda eng PBKL bicssc Axler, Sheldon verfasserin aut Measure, Integration & Real Analysis Cham Springer Nature 2020 1 Online-Ressource (411 p.) Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Graduate Texts in Mathematics Open Access Unrestricted online access star This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online All rights reserved English Integral calculus & equations Integral calculus and equations https://library.oapen.org/bitstream/id/ce19d94d-b8b6-420f-9e69-d9f565703c26/1007045.pdf X:OAPEN Verlag OAPEN Library: download the publication kostenfrei http://library.oapen.org/handle/20.500.12657/23111 X:OAPEN Verlag OAPEN Library: description of the publication kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280043752 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280599211 OLR-OAPEN f z 01-03-23 30 01 0104 4280958688 GBV-OAPEN z 01-03-23 31 01 0027 4280234000 z 01-03-23 34 01 3551 427879777X OLR-OAPEN zi002 01-03-23 39 01 0547 4281149457 GBV-OAPEN ke 01-03-23 40 01 0007 4279866279 OLR-OAPEN xsn 01-03-23 63 01 3401 4281529292 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281751033 OLR-OAPEN z 01-03-23 70 01 0089 4280420300 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278616511 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343142787 OLR-OAL Vervielfältigungen (z.B. 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Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. 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Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. 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