{"product_id":"measure-and-integration-isbn-9780470259542","title":"Measure and Integration","description":"A 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\u003c\/li\u003e \u003cli\u003eProduct measures and Fubini's theorem\u003c\/li\u003e \u003cli\u003eDifferentiation theorems for functions of real variables\u003c\/li\u003e \u003cli\u003eDecomposition theorems for signed measures\u003c\/li\u003e \u003cli\u003eAbsolute continuity and the Radon-Nikodym theorem\u003c\/li\u003e \u003cli\u003eLp spaces, continuous-function spaces, and duality theorems\u003c\/li\u003e \u003cli\u003eTranslation-invariant subspaces of L2 and applications\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe book's presentation lays the foundation for further study of functional analysis, harmonic analysis, and probability, and its treatment of real analysis highlights the fundamental role of translations. Each theorem is accompanied by opportunities to employ the concept, as numerous exercises explore applications including convolutions, Fourier transforms, and differentiation across the integral sign.\u003c\/p\u003e \u003cp\u003eProviding an efficient and readable treatment of this classical subject, \u003ci\u003eMeasure and Integration: A Concise Introduction to Real Analysis\u003c\/i\u003e is a useful book for courses in real analysis at the graduate level. It is also a valuable reference for practitioners in the mathematical sciences.\u003c\/p\u003e Preface. \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 Rn.\u003c\/p\u003e \u003cp\u003e3.6 Jordan Measure in Rn.\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 L1 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 Lp.\u003c\/p\u003e \u003cp\u003e9.2 The Dual of a Banach Space.\u003c\/p\u003e \u003cp\u003e9.3 The Dual Space of Lp.\u003c\/p\u003e \u003cp\u003e9.4 Hilbert Space, Its Dual, and L2.\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 L2(T).\u003c\/p\u003e \u003cp\u003e10.2 Closed Invariant Subspaces of L2(T).\u003c\/p\u003e \u003cp\u003e10.3 Schwartz Functions: Fourier Transform and Inversion.\u003c\/p\u003e \u003cp\u003e10.4 Closed, Invariant Subspaces of L2(R).\u003c\/p\u003e \u003cp\u003e10.5 Irreducibility of L2(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 \"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) \u003cb\u003eLeonard F. Richardson, PhD\u003c\/b\u003e, is Herbert Huey McElveen Professor and Director of Graduate Studies in Mathematics at Louisiana State University, where he is also Assistant Chair of the Department of Mathematics. Dr. Richardson's research interests include harmonic analysis, homogeneous spaces, and representation theory. He is the author of \u003ci\u003eAdvanced Calculus: An Introduction to Linear Analysis\u003c\/i\u003e, also published by Wiley. \u003cb\u003eA uniquely accessible book for general measure and integration, emphasizing the real line, Euclidean space, and the underlying role of translation in real analysis\u003c\/b\u003e \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\u003c\/li\u003e \u003cli\u003eProduct measures and Fubini's theorem\u003c\/li\u003e \u003cli\u003eDifferentiation theorems for functions of real variables\u003c\/li\u003e \u003cli\u003eDecomposition theorems for signed measures\u003c\/li\u003e \u003cli\u003eAbsolute continuity and the Radon-Nikodym theorem\u003c\/li\u003e \u003cli\u003eLp spaces, continuous-function spaces, and duality theorems\u003c\/li\u003e \u003cli\u003eTranslation-invariant subspaces of L2 and applications\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe book's presentation lays the foundation for further study of functional analysis, harmonic analysis, and probability, and its treatment of real analysis highlights the fundamental role of translations. Each theorem is accompanied by opportunities to employ the concept, as numerous exercises explore applications including convolutions, Fourier transforms, and differentiation across the integral sign.\u003c\/p\u003e \u003cp\u003eProviding an efficient and readable treatment of this classical subject, \u003ci\u003eMeasure and Integration: A Concise Introduction to Real Analysis\u003c\/i\u003e is a useful book for courses in real analysis at the graduate level. It is also a valuable reference for practitioners in the mathematical sciences.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989592752357,"sku":"NP9780470259542","price":129.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470259542.jpg?v=1761784731","url":"https:\/\/k12savings.com\/products\/measure-and-integration-isbn-9780470259542","provider":"K12savings","version":"1.0","type":"link"}