000 | 04321nam a22005055i 4500 | ||
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001 | 978-3-030-33143-6 | ||
003 | DE-He213 | ||
005 | 20210511121200.0 | ||
007 | cr nn 008mamaa | ||
008 | 191129s2020 gw | s |||| 0|eng d | ||
020 |
_a9783030331436 _9978-3-030-33143-6 |
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024 | 7 |
_a10.1007/978-3-030-33143-6 _2doi |
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050 | 4 | _aQA312-312.5 | |
072 | 7 |
_aPBKL _2bicssc |
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072 | 7 |
_aMAT034000 _2bisacsh |
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072 | 7 |
_aPBKL _2thema |
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082 | 0 | 4 |
_a515.42 _223 |
100 | 1 |
_aAxler, Sheldon. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _92191 |
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245 | 1 | 0 |
_aMeasure, Integration & Real Analysis _h[electronic resource] / _cby Sheldon Axler. |
250 | _a1st ed. 2020. | ||
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2020. |
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300 |
_aXVIII, 411 p. 41 illus., 20 illus. in color. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aGraduate Texts in Mathematics, _x0072-5285 ; _v282 |
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505 | 0 | _aAbout the Author -- Preface for Students -- Preface for Instructors -- Acknowledgments -- 1. Riemann Integration -- 2. Measures -- 3. Integration -- 4. Differentiation -- 5. Product Measures -- 6. Banach Spaces -- 7. L^p Spaces -- 8. Hilbert Spaces -- 9. Real and Complex Measures -- 10. Linear Maps on Hilbert Spaces -- 11. Fourier Analysis -- 12. Probability Measures -- Photo Credits -- Bibliography -- Notation Index -- Index -- Colophon: Notes on Typesetting. | |
506 | 0 | _aOpen Access | |
520 | _aThis 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. | ||
650 | 0 |
_aMeasure theory. _91427 |
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650 | 1 | 4 |
_aMeasure and Integration. _0https://scigraph.springernature.com/ontologies/product-market-codes/M12120 _91434 |
710 | 2 |
_aSpringerLink (Online service) _9141 |
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776 | 0 | 8 |
_iPrinted edition: _z9783030331429 |
776 | 0 | 8 |
_iPrinted edition: _z9783030331443 |
830 | 0 |
_aGraduate Texts in Mathematics, _x0072-5285 ; _v282 _9330 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-030-33143-6 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-SXMS | ||
912 | _aZDB-2-SOB | ||
942 |
_cEBK _w1 _xAdministrator Library _y1 _z Administrator Library |
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999 |
_c1150 _d1150 |
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773 | _tSpringer Nature Open Access eBook |