本书是经典的Carus Monograph系列（畅销超过25年）中，关于实变函数论的一个修订、更新和增强的版本，本书的早期版本内容包括集合、度量空间、连续函数和可微函数。
第四版增加了可测集与函数、Lebesgue积分与Stieltjes积分、应用等内容，保持了之前版本轻松友好的叙事风格，供有一定数学素养和微积分背景的读者阅读。本书既适合自学，也适合用作高等微积分或实分析课程的补充材料，它不是一部系统性专著，而是与实函数相关的各种有趣主题的系列讲座，其中许多主题在本科教材中并不常见，例如，处处连续的振荡函数的存在性（借助于Baire范畴定理），通用弦定理，两个函数有相同导数却不相差一个常数，以及Stieltjes积分在求无穷级数收敛速度中的应用。
本书重现了学科发展早期的那种奇妙的感觉，是数学图书馆的必备藏书。

Preface to the Fourth Edition
Preface to the Third Edition
1 Sets
1 Sets
2 Sets of real numbers
3 Countable and uncountable sets
4 Metric spaces
5 Open and closed sets
6 Dense and nowhere dense sets
7 Compactness
8 Convergence and completeness
9 Nested sets and Baire's theorem
10 Some applications of Baire's Theorem
11 Sets of measure zero
2 Functions
12 Functions
13 Continuous functions.
14 Properties of continuous functions
15 Upper and lower limits
16 Sequences of functions
17 Uniform convergence
18 Pointwise limits of continuous functions
19 Approximations to continuous functions
20 Linear functions
21 Derivatives
22 Monotonic functions
23 Convex functions
24 Infinitely differentiable functions
3 Integration
25 Lebesgue measure
26 Measurable functions
27 Definition of the Lebesgue integral
28 Properties of Lebesgue integrals
29 Applications of the Lebesgue integral
30 Stieltjes integrals
31 Applications of the Stieltjes integral
32 Partial sums of infinite series
Answers to Exercises
Index