{"product_id":"measure-and-integration-9780470259542","title":"Measure and Integration","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA uniquely accessible book for general measure and integration, emphasizing the real line, Euclidean space, and the underlying role of translation in real analysis  \u003cp\u003e\u003ci\u003eMeasure and Integration: A Concise Introduction to Real Analysis\u003c\/i\u003e presents the basic concepts and methods that are important for successfully reading and understanding proofs. Blending coverage of both fundamental and specialized topics, this book serves as a practical and thorough introduction to measure and integration, while also facilitating a basic understanding of real analysis.\u003c\/p\u003e \u003cp\u003eThe author develops the theory of measure and integration on abstract measure spaces with an emphasis of the real line and Euclidean space. Additional topical coverage includes:\u003c\/p\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eMeasure spaces, outer measures, and extension theorems\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003eLebesgue measure on the line and in Euclidean space\u003c\/li\u003e \u003cli\u003eMeasurable functions, Egoroff''s theorem, and Lusin''s theorem\u003c\/li\u003e \u003cli\u003eConvergence theorems for integrals\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The book is well thought out, organized and written. It has all the results in measure theory that are necessary for both pure and applied mathematics research.\" (Mathematical Reviews, 2011)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003eAcknowledgments.\u003c\/p\u003e \u003cp\u003eIntroduction.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 History of the Subject.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 History of the Idea.\u003c\/p\u003e \u003cp\u003e1.2 Deficiencies of the Riemann Integral.\u003c\/p\u003e \u003cp\u003e1.3 Motivation for the Lebesgue Integral.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Fields, Borel Fields and Measures.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Fields, Monotone Classes, and Borel Fields.\u003c\/p\u003e \u003cp\u003e2.2 Additive Measures.\u003c\/p\u003e \u003cp\u003e2.3 Carathéodory Outer Measure.\u003c\/p\u003e \u003cp\u003e2.4 E. Hopf’s Extension Theorem.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Lebesgue Measure.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Finite Interval [-N,N).\u003c\/p\u003e \u003cp\u003e3.2 Measurable Sets, Borel Sets, and the Real Line.\u003c\/p\u003e \u003cp\u003e3.3 Measure Spaces and Completions.\u003c\/p\u003e \u003cp\u003e3.4 Semimetric Space of Measurable Sets.\u003c\/p\u003e \u003cp\u003e3.5 Lebesgue Measure in R\u003csup\u003en\u003c\/sup\u003e.\u003c\/p\u003e \u003cp\u003e3.6 Jordan Measure in R\u003csup\u003en\u003c\/sup\u003e.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Measurable Functions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Measurable Functions.\u003c\/p\u003e \u003cp\u003e4.2 Limits of Measurable Functions.\u003c\/p\u003e \u003cp\u003e4.3 Simple Functions and Egoroff’s Theorem.\u003c\/p\u003e \u003cp\u003e4.4 Lusin’s Theorem.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 The Integral.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Special Simple Functions.\u003c\/p\u003e \u003cp\u003e5.2 Extending the Domain of the Integral.\u003c\/p\u003e \u003cp\u003e5.3 Lebesgue Dominated Convergence Theorem.\u003c\/p\u003e \u003cp\u003e5.4 Monotone Convergence and Fatou’s Theorem.\u003c\/p\u003e \u003cp\u003e5.5 Completeness of L\u003csup\u003e1\u003c\/sup\u003e and the Pointwise Convergence Lemma.\u003c\/p\u003e \u003cp\u003e5.6 Complex Valued Functions.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Product Measures and Fubini’s Theorem.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Product Measures.\u003c\/p\u003e \u003cp\u003e6.2 Fubini’s Theorem.\u003c\/p\u003e \u003cp\u003e6.3 Comparison of Lebesgue and Riemann Integrals.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Functions of a Real Variable.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Functions of Bounded Variation.\u003c\/p\u003e \u003cp\u003e7.2 A Fundamental Theorem for the Lebesgue Integral.\u003c\/p\u003e \u003cp\u003e7.3 Lebesgue’s Theorem and Vitali’s Covering Theorem.\u003c\/p\u003e \u003cp\u003e7.4 Absolutely Continuous and Singular Functions.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 General Countably Additive Set Functions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Hahn Decomposition Theorem.\u003c\/p\u003e \u003cp\u003e8.2 Radon-Nikodym Theorem.\u003c\/p\u003e \u003cp\u003e8.3 Lebesgue Decomposition Theorem.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Examples of Dual Spaces from Measure Theory.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Banach Space L\u003csup\u003ep\u003c\/sup\u003e.\u003c\/p\u003e \u003cp\u003e9.2 The Dual of a Banach Space.\u003c\/p\u003e \u003cp\u003e9.3 The Dual Space of L\u003csup\u003ep\u003c\/sup\u003e.\u003c\/p\u003e \u003cp\u003e9.4 Hilbert Space, Its Dual, and L\u003csup\u003e2\u003c\/sup\u003e.\u003c\/p\u003e \u003cp\u003e9.5 Riesz-Markov-Saks-Kakutani Theorem.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Translation Invariance in Real Analysis.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 An Orthonormal Basis for L\u003csup\u003e2\u003c\/sup\u003e(T).\u003c\/p\u003e \u003cp\u003e10.2 Closed Invariant Subspaces of L\u003csup\u003e2\u003c\/sup\u003e(T).\u003c\/p\u003e \u003cp\u003e10.3 Schwartz Functions: Fourier Transform and Inversion.\u003c\/p\u003e \u003cp\u003e10.4 Closed, Invariant Subspaces of L\u003csup\u003e2\u003c\/sup\u003e(R).\u003c\/p\u003e \u003cp\u003e10.5 Irreducibility of L\u003csup\u003e2\u003c\/sup\u003e(R) Under Translations and Rotations.\u003c\/p\u003e \u003cp\u003eAppendix A: The Banach-Tarski Theorem.\u003c\/p\u003e \u003cp\u003eA.1 The Limits to Countable Additivity.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402309706071,"sku":"9780470259542","price":90.86,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470259542.jpg?v=1730480024","url":"https:\/\/bookcurl.com\/products\/measure-and-integration-9780470259542","provider":"Book Curl","version":"1.0","type":"link"}