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,...
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| Format: | Online |
| Język: | angielski |
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Springer Nature
2021
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| Hasła przedmiotowe: | |
| Dostęp online: | 1007045 |
| Etykiety: |
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| _version_ | 1869527798195945472 |
|---|---|
| author | Axler, Sheldon |
| author_browse | Axler, Sheldon |
| author_facet | Axler, Sheldon |
| author_sort | Axler, Sheldon |
| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-39003 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-390032025-03-24T05:59:50Z Measure, Integration & Real Analysis Axler, Sheldon Mathematics Measure theory Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKL Integral calculus and equations 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. 2021-02-10T15:00:50Z 2021-02-10T15:00:50Z 2020-03-18 13:36:15 2020-04-01T09:04:01Z 2020 book 1007045 OCN: 1129397508 http://library.oapen.org/handle/20.500.12657/23111 https://directory.doabooks.org/handle/20.500.12854/39003 eng Graduate Texts in Mathematics open access image/jpeg image/jpeg image/jpeg image/jpeg https://library.oapen.org/bitstream/20.500.12657/23111/1/1007045.pdf https://library.oapen.org/bitstream/20.500.12657/23111/1/1007045.pdf https://library.oapen.org/bitstream/20.500.12657/23111/1/1007045.pdf https://library.oapen.org/bitstream/20.500.12657/23111/1/1007045.pdf Springer Nature 10.1007/978-3-030-33143-6 10.1007/978-3-030-33143-6 9fa3421d-f917-4153-b9ab-fc337c396b5a 411 Cham open access |
| spellingShingle | Mathematics Measure theory Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKL Integral calculus and equations Axler, Sheldon Measure, Integration & Real Analysis |
| title | Measure, Integration & Real Analysis |
| title_full | Measure, Integration & Real Analysis |
| title_fullStr | Measure, Integration & Real Analysis |
| title_full_unstemmed | Measure, Integration & Real Analysis |
| title_short | Measure, Integration & Real Analysis |
| title_sort | measure integration real analysis |
| topic | Mathematics Measure theory Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKL Integral calculus and equations |
| topic_facet | Mathematics Measure theory Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKL Integral calculus and equations |
| url | 1007045 |
| work_keys_str_mv | AT axlersheldon measureintegrationrealanalysis |