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This title in other editionsOther titles in the Cambridge Studies in Advanced Mathematics series:
Cambridge Studies in Advanced Mathematics #74: Real Analysis and Probabilityby R. M. Dudley
Synopses & ReviewsPublisher Comments:This classic textbook, now reissued, offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The new edition has been made even more selfcontained than before; it now includes a foundation of the real number system and the StoneWeierstrass 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.
Book News Annotation:This is a reissue of textbook covering graduate level courses in probability theory and real analysis, each conceived as a onesemester course. Dudley (Massachusetts Institute of Technology), in an effort to make the text selfcontained, has added a treatment of the Stone Weierstrass theorem.
Annotation c. Book News, Inc., Portland, OR (booknews.com) Synopsis:This classic text, now reissued in paperback, offers a clear exposition of modern probability theory.
Synopsis:Includes bibliographical references and indexes.
Table of Contents1. Foundations: set theory; 2. General topology; 3. Measures; 4. Integration; 5. Lp spaces: introduction to functional analysis; 6. Convex sets and duality of normed spaces; 7. Measure, topology, and differentiation; 8. Introduction to probability theory; 9. Convergence of laws and central limit theorems; 10. Conditional expectations and martingales; 11. Convergence of laws on separable metric spaces; 12. Stochastic processes; 13. Measurability: Borel isomorphism and analytic sets; Appendixes: A. Axiomatic set theory; B. Complex numbers, vector spaces, and Taylor's theorem with remainder; C. The problem of measure; D. Rearranging sums of nonnegative terms; E. Pathologies of compact nonmetric spaces; Indices.
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