Real Analysis and Probability Theory (English Edition, Second Edition)

Author: Dudley
Publisher:
Publish Date: 2006-07-01
Features: This book has achieved excellent success in two aspects. First, it is a comprehensive and novel textbook on real analysis. Second, it is a complete and self-contained textbook on probability theory. The book undoubtedly sets a new standard for rigor and completeness. — American Mathematical Society bulletin
This is an extraordinary work. In both teaching and reference, it will become a standardized textbook, providing a comprehensive introduction to the knowledge of real analysis with proofs throughout the book. Some topics and proofs are rarely seen in other textbooks. — Edinburgh Mathematical Society bulletin
Rigorous, profound, and novel, this is a textbook suitable for graduate students in mathematics. — ISI brief book review
This is a highly acclaimed textbook that clearly explains modern probability theory and the interaction between metric spaces and probability measures. The book is divided into two parts. The first part introduces the content of real analysis, including basic set theory, general topology, measure theory, integration, Banach spaces, and an introduction to functional analysis in topological spaces, convex sets and functions, and measures on topological spaces. The second part introduces the content of probability based on measure theory, including the law of large numbers, ergodic theorems, central limit theorems, conditional expectations, and martingale convergence. Additionally, the chapter on stochastic processes (Chapter 12) introduces Brownian motion and Brownian bridges. Compared to the previous edition, this edition is more complete, introducing the foundations of the real number system and the Stone-Weierstrass theorem on uniform approximation in functional algebra from the beginning; several sections have been revised and improved, and historical notes have been expanded; many new exercises have been added, as well as hints for solutions to some exercises.