这是一本广受称赞的教科书，清晰地讲解了现代概率论以及度量空间与概率测度之间的相互作用。本书分两部分，**部分介绍了实分析的内容，包括基本集合论、一般拓扑学、测度论、积分法、巴拿赫空间和拓扑空间中的泛函分析导论、凸集和函数、拓扑空间上的测度等。第二部分介绍了基于测度论的概率方面的内容，包括大数律、遍历定理、**极限定理、条件期望、鞅收敛等。另外，随机过程一章 (第12章) 还介绍了布朗运动和布朗桥。
与前版相比，本版内容更完善，一开始就介绍了实数系的基础和泛代数中的一致逼近的斯通-魏尔斯特拉斯定理；修订和改进了几节的内容，扩充了大量历史注记；增加了很多新的习题，以及对一些习题的解答的提示。

Preface to the cambridge Edition
1. Foundations: set theory
1.1 definitions for Set Theory and the Real Number System
1.2 Relations and Orderings
1.3 Transfinite Induction and Recursion
1.4 Cardinality
1.5 The Axiom of Choice and Its Equivalents
2. General topology
2.1 Toplogies,Metrics,and Continuity
2.2 Compactness and Product Toplogies
2.3 Complete and Compact Metric Spaces
2.4 Some metrics for Function Spaces
2.5 Completion and Completeness of Metric Spaces
2.6 Extension of Continuous Functions
2.7 Uniformities and Uniform Spaces
2.8 Compactification
3. Measures
3.1 Introduction to Measures
3.2 Semirings and Rings
3.3 Completion of Measures
3.4 Lebesgue Measure and Nonmeasurable Sets
3.5 Atomic and Nonatomic Measures
4. Integration
4.1 Simple Functions
4.2 Measurability
4.3 Convergence Theorems for Integrals
4.4 Product Measures
4.5 Daniell-Stone Integrals
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
Appendixes: B. Complex numbers, vector spaces, and Taylor’s theorem with remainder
Appendixes: C. The problem of measure
Appendixes: D. Rearranging sums of Nonnegative terms
Appendixes: E. Pathologies of compact Nonmetric spaces
Author Index
Subject Index
Notation Index

本书在两个方面获得了**的成功。一是它是一本全面、新颖的实分析教程，二是它是一本数学理论完整和自成体系的概率论教程。本书无疑给出了一种严谨和完整的新标准。
——美国数学会公报
这是一本非凡的著作。在教学和参考两个方面本书将成为一本标准化教材，它全面地介绍了实分析的**知识，且证明贯穿全书。一些主题和证明极少在其他教科书中见到。
——爱丁堡数学会学报
严谨，精深，新颖，这是一本适用于数学专业研究生的教材。
——ISI的简短书评