内容简介

《实分析原理(第3版)》主要内容：This is the third edition of Principles of Real Alysis, first published in 1981. The aim of this edition is to accommodate the current needs for the traditional real analysis course that is usually taken by the senior undergraduate or by the first year graduate student in mathematics. This edition differs substantially from the second edition. Each chapter has been greatly improved by incorporating new material and by rearranging the old material. Moreover, a new chapter （Chapter 6） on Hilbert spaces and Fourier analysis has been added.1

本书主要用统一、联系的观点看待现代分析，把现代分析的不同分支领域视为高度相互联系而非分离的学科。通过这些联系可以使读者在整体上对现代分析这一学科有更好的理解。

目录

Preface

CHAPTER 1. FUNDAMENTALS OF REAL ANALYSIS

1. Elementary Set Theory

2. Countable and Uncountable Sets

3. The Real Numbers

4. Sequences of Real Numbers

5. The Extended Real Numbers

6. Metric Spaces

7. Compactness in Metric Spaces

CHAPTER 2. TOPOLOGY AND CONTINUITY

8. Topological Spaces

9. Continuous Real-Valued Functions

10. Separation Properties of Continuous Functions

11. The Stone-Weierstrass Approximation Theorem

CHAPTER 3. THE THEORY OF MEASURE