Real Analysis: Measure Theory, Integration, and Hilbert Spaces
Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and H...
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| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2009]
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| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 UPA01 URL des Erstveröffentlichers |
| Zusammenfassung: | Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Nov 2019) |
| Beschreibung: | 1 online resource (424 pages) 51 line illus |
| ISBN: | 9781400835560 |
| DOI: | 10.1515/9781400835560 |
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| 520 | |a Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Stein, Elias M. 1931-2018 Shakarchi, Rami |
| author_GND | (DE-588)119278596 |
| author_facet | Stein, Elias M. 1931-2018 Shakarchi, Rami |
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| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400835560 |
| format | Electronic eBook |
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| spelling | Stein, Elias M. 1931-2018 (DE-588)119278596 aut Real Analysis Measure Theory, Integration, and Hilbert Spaces Rami Shakarchi, Elias M. Stein Princeton, NJ Princeton University Press [2009] © 2005 1 online resource (424 pages) 51 line illus txt rdacontent c rdamedia cr rdacarrier Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Nov 2019) Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis In English MATHEMATICS / Mathematical Analysis bisacsh Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Reelle Analysis (DE-588)4627581-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Maßtheorie (DE-588)4074626-4 s 2\p DE-604 Reelle Analysis (DE-588)4627581-2 s 3\p DE-604 Integrationstheorie (DE-588)4138369-2 s 4\p DE-604 Shakarchi, Rami aut aut https://doi.org/10.1515/9781400835560 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stein, Elias M. 1931-2018 Shakarchi, Rami Real Analysis Measure Theory, Integration, and Hilbert Spaces MATHEMATICS / Mathematical Analysis bisacsh Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd Reelle Analysis (DE-588)4627581-2 gnd |
| subject_GND | (DE-588)4138369-2 (DE-588)4074626-4 (DE-588)4627581-2 (DE-588)4151278-9 |
| title | Real Analysis Measure Theory, Integration, and Hilbert Spaces |
| title_auth | Real Analysis Measure Theory, Integration, and Hilbert Spaces |
| title_exact_search | Real Analysis Measure Theory, Integration, and Hilbert Spaces |
| title_full | Real Analysis Measure Theory, Integration, and Hilbert Spaces Rami Shakarchi, Elias M. Stein |
| title_fullStr | Real Analysis Measure Theory, Integration, and Hilbert Spaces Rami Shakarchi, Elias M. Stein |
| title_full_unstemmed | Real Analysis Measure Theory, Integration, and Hilbert Spaces Rami Shakarchi, Elias M. Stein |
| title_short | Real Analysis |
| title_sort | real analysis measure theory integration and hilbert spaces |
| title_sub | Measure Theory, Integration, and Hilbert Spaces |
| topic | MATHEMATICS / Mathematical Analysis bisacsh Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | MATHEMATICS / Mathematical Analysis Integrationstheorie Maßtheorie Reelle Analysis Einführung |
| url | https://doi.org/10.1515/9781400835560 |
| work_keys_str_mv | AT steineliasm realanalysismeasuretheoryintegrationandhilbertspaces AT shakarchirami realanalysismeasuretheoryintegrationandhilbertspaces |