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Cambridge Studies in Advanced Mathematics #74: Real Analysis and Probabilityby R. M. Dudley
Synopses & Reviews
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 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.
Book News Annotation:
This is a reissue of textbook covering graduate level courses in probability theory and real analysis, each conceived as a one-semester course. Dudley (Massachusetts Institute of Technology), in an effort to make the text self-contained, has added a treatment of the Stone- Weierstrass theorem.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
This classic text, now reissued in paperback, offers a clear exposition of modern probability theory.
Includes bibliographical references and indexes.
Table of Contents
1. 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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