本书由在国际上享有盛誉普林斯大林顿大学教授Stein等撰写而成，是一部为数学及相关专业大学二年级和三年级学生编写的教材，理论与实践并重。为了便于非数学专业的学生学习，全书内容简明、易懂,读者只需掌握微积分和线性代数知识。关于本书的详细介绍，请见“影印版前言”。
本书已被哈佛大学和加利福尼亚理工学院选为教材。与本书相配套的教材《傅立叶分析导论》和《复分析》也已影印出版。
作者简介
Stein，在国际上享有盛誉，现任美国普林斯顿大学数学系教授。 他是当代分析，特别是调和分析和分析领域领袖人物之一。古典调和分析最困难问题之一是推广到多维。他是多维欧氏调和分析的创造者之一，为此他发展了许多先进工具如奇异积分、Radon变换、极大函数等。他还发
目录
Foreword
Introduction
1 Fourier series: completion
2 Limits of continuous functions
3 Length of curves
4 Differentiation and integration
5 The problem of measure
Chapter 1. Measure Theory
1 Preliminaries
2 The exterior measure
3 Measurable sets and the Lebesgue measure4 Measurable functions
4.1 Definition and basic properties
4.2 Approximation by simple functions or step functions4.3 Littlewood's three principles
5* The Brunn-Minkowski inequality
6 Exercises
7 Problems
Chapter 2. Integration Theory
1 The Lebesgue integral: basic properties and convergence theorems2 The space L1 of integrable functions
3 Fubini's theorem
3.1 Statement and proof of the theorem
3.2 Applications of Fubini's theorem
4* A Fourier inversion formula
5 Exercises
6 Problems
Chapter 3. Differentiation and Integration1 Differentiation of the integral
1.1 The Hardy-Littlewood maximal function1.2 The Lebesgue differentiation theorem
2 Good kernels and approximations to the identity3 Differentiability of functions
3.1 Functions of bounded variation
3.2 Absolutely continuous functions
3.3 Differentiability of jump functions
4 Rectifiable curves and the isoperimetric inequality4.1 Minkowski content of a curve
4.2* Isoperimetrie inequality
5 Exercises
6 Problems
Chapter 4. Hilbert Spaces: An Introduction1 The Hilbert space L2
2 Hilbert spaces
2.1 Orthogonality
2.2 Unitary mappings
2.3 Pre-Hilbert spaces
3 Fourier series and Fatou's theorem
3.1 Fatou's theorem
4 Closed subspaees and orthogonal projections5 Linear transformations
5.1 Linear flmetionals and the Riesz representation the-orem5.2 Adjoints
5.3 Examples
6 Compact operators
7 Exercises
8 Problems
Chapter 5. Hilbert Spaces: Several Examples1 The Fourier transform on L2
2 The Hardy space of the upper half-plane3 Constant coefficient partial differential equations3.1 Weak solutions
3.2 The main theorem and key estimate
4* The Dirichlet principle
4.1 Harmonic functions
4.2 The boundary value problem and Diriehlet's principle5 Exercises
6 Problems
Chapter 6.Abstract Measure and Integration TheoryChapter 7.Hausdorff Measure and Fractals
Notes and References
Bibliography
Symbol Glossary
Index
