000 04321nam a22005055i 4500
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
024 7 _a10.1007/978-3-030-33143-6
_2doi
050 4 _aQA312-312.5
072 7 _aPBKL
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKL
_2thema
082 0 4 _a515.42
_223
100 1 _aAxler, Sheldon.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_92191
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.
300 _aXVIII, 411 p. 41 illus., 20 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v282
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
650 1 4 _aMeasure and Integration.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M12120
_91434
710 2 _aSpringerLink (Online service)
_9141
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
999 _c1150
_d1150
773 _tSpringer Nature Open Access eBook