{"product_id":"real-analysis-and-probability-hardback-9780521809726","title":"Real Analysis and Probability (Hardback) 9780521809726","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eReal Analysis and Probability\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis classic text offers a clear exposition of modern probability theory.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eR. M. Dudley (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521809726, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 14 October 2002\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e568 pages, 400 exercises\u003cbr\u003e23.7 x 16 x 3.4 cm, 0.896 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'The book serves as a clear, rigorous, and complete introduction to modern probability theory using methods of mathematical analysis, and a description of relations between the two fields … it could be very  useful for students interested in learning both topics, it can also serve as complementary reading to standard lectures. Teachers preparing their graduate level courses can use the book as an excellent, rigorously written and complete source.' EMS Newsletter\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Foundations: set theory\u003cbr\u003e 2. General topology\u003cbr\u003e 3. Measures\u003cbr\u003e 4. Integration\u003cbr\u003e 5. Lp spaces: introduction to functional analysis\u003cbr\u003e 6. Convex sets and duality of normed spaces\u003cbr\u003e 7. Measure, topology, and differentiation\u003cbr\u003e 8. Introduction to probability theory\u003cbr\u003e 9. Convergence of laws and central limit theorems\u003cbr\u003e 10. Conditional expectations and martingales\u003cbr\u003e 11. Convergence of laws on separable metric spaces\u003cbr\u003e 12. Stochastic processes\u003cbr\u003e 13. Measurability: Borel isomorphism and analytic sets\u003cbr\u003e Appendixes: A. Axiomatic set theory\u003cbr\u003e B. Complex numbers, vector spaces, and Taylor's theorem with remainder\u003cbr\u003e C. The problem of measure\u003cbr\u003e D. Rearranging sums of nonnegative terms\u003cbr\u003e E. Pathologies of compact nonmetric spaces\u003cbr\u003e Indices.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Probability \u0026amp; statistics [\u003ca title=\"See our other books on Probability \u0026amp; statistics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Probability%20\u0026amp;%20statistics%20%5BPBT%5D%22\"\u003ePBT\u003c\/a\u003e], Real analysis, real variables [\u003ca title=\"See our other books on Real analysis, real variables\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Real%20analysis,%20real%20variables%20%5BPBKB%5D%22\"\u003ePBKB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46004801208600,"sku":"9780521809726","price":166.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521809726i_c22f525d-28a5-427f-977b-3ef66f5c19b3.jpg?v=1691368267","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/real-analysis-and-probability-hardback-9780521809726","provider":"Freshly Printed Books","version":"1.0","type":"link"}