000			03302nam a22003617a 4500
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005			20240508175041.0
008			240506b |||||||| |||| 00| 0 hin d
020			_a9783030331429
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082			_a517 _bAXL-M
100			_aAxler, Sheldon.
245			_aMeasure, integration and real analysis
260			_aNew York : _bSpringer, _c2020.
300			_axviii, 411p. : _billustrations (colour) ; _c25 cm.
490			_aGraduate texts in mathematics ; _v282 _x0072-5285
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			_aMathematics
650			_aMeasure Theory
650			_aIntegration, Functional
650			_aMathematical Analysis
650			_aRiemann Integration
650			_aLebesgue Integration
650			_aLebesgue Differentiation Theorem
650			_aBanach Spaces
650			_aHilbert Spaces
650			_aRiesz Representation Theorem
856			_3Table of contents _uhttps://link.springer.com/book/10.1007/978-3-030-33143-6#toc
856			_3Reviews _uhttps://www.goodreads.com/book/show/51019857-measure-integration-real-analysis?from_search=true&from_srp=true&qid=9ZzDJkqdUz&rank=1#CommunityReviews
856			_3Electronic version _uhttps://link.springer.com/book/10.1007/978-3-030-33143-6#bibliographic-information
942			_cBK _2udc
999			_c34979 _d34979