Real analysis and probability [electronic resource]
 Responsibility
 R.M. Dudley.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2002.
 Physical description
 x, 555 p.
 Series
 Cambridge studies in advanced mathematics ; 74.
Online
Course reserve
 Course
 MATH230B01  Theory of Probability
 Instructor(s)
 Dembo, Amir
 Course
 STATS310B01  Theory of Probability II
 Instructor(s)
 Dembo, Amir
More options
Description
Creators/Contributors
 Author/Creator
 Dudley, R. M. (Richard M.)
 Contributor
 ProQuest (Firm)
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 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.
 (source: Nielsen Book Data)
 Summary

This 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 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2002
 Series
 Cambridge studies in advanced mathematics ; 74
 Reproduction
 Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.
 ISBN
 052180972X (hardback)
 0521007542 (pbk.)
 0511042086 (electronic bk.)
 9780511042089 (electronic bk.)
 0511044887
 9780511044885
 9780521007542 (pbk.)
 9780521809726 (hardback)
 9786610419425
 6610419426