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本书是分析领域内的一部经典著作。主要内容包括：抽象积分、正博雷尔测度、LP-空间、希尔伯特空间的初等理论、巴拿赫空间技巧的例子、复测度、微分、积空间上的积分、傅里叶变换、全纯函数的初等性质、调和函数、*大模原理、有理函数逼近、共形映射、全纯函数的零点、解析延拓、HP-空间、巴拿赫代数的初等理论、全纯傅里叶变换、用多项式一致逼近等。另外，书中还附有大量设计巧妙的习题。本书体例优美，实用性很强，列举的实例简明精彩，基本上对所有给出的命题都进行了论证，适合作为高等院校数学专业高年级本科生和研究生的教材。

《实分析与复分析（英文版）》目录：

Preface

Prologue: The Exponential Function

Chapter 1 Abstract Integration

Set-theoretic notations and terminology

The concept of measurability

Simple functions

Elementary properties of measures

Arithmetic in [0, ]

Integration of positive functions

Integration of complex functions

The role played by sets of measure zero

Exercises

Chapter 2 Positive Borel Measures

Vector spaces

Topological preliminaries

The Riesz representation theorem

Regularity properties of Borel measures

Lebesgue measure

Continuity properties of measurable functions

Exercises

Chapter 3 LP-Spaces

Convex functions and inequalities

The Lp-spaces

Approximation by continuous functions

Exercises

Chapter 4 Elementary Hilbert Space Theory

Inner products and linear functionals

Orthonormal sets

Trigonometric series

Exercises

Chapter 5 Examples of Banach Space Techniques

Banach spaces

Consequences of Baire's theorem

Fourier series of continuous functions

Fourier coefficients of L1-functions

The Hahn-Banach theorem

An abstract approach to the Poisson integral

Exercises

Chapter 6 Complex Measures

Total variation

Absolute continuity

Consequences of the Radon-Nikodym theorem

Bounded linear functionals on Lp

The Riesz representation theorem

Exercises

Chapter 7 Differentiation

Derivatives of measures

The fundamental theorem of Calculus

Differentiable transformations

Exercises

Chapter 8 Integration on Product Spaces

Measurability on cartesian products

Product measures

The Fubini theorem

Completion of product measures

Convolutions

Distribution functions

Exercises

Chapter 9 Fourier Transforms

Formal properties

The inversion theorem

The Plancherel theorem

The Banach algebra L1

Exercises

Chapter 10 Elementary Properties of Holomorphic

Functions

Complex differentiation

Integration over paths

The local Cauchy theorem

The power series representation

The open mapping theorem

The global Cauchy theorem

The calculus of residues

Exercises

Chapter 11 Harmonic Functions

The Cauchy-Riemann equations

The Poisson integral

The mean value property

Boundary behavior of Poisson integrals

Representation theorems

Exercises

Chapter 12 The Maximum Modulus Principle

Introduction

The Schwarz lemma

The Phragmen-Lindelof method

An interpolation theorem

A converse of the maximum modulus theorem

Exercises

Chapter 13 Approximation by Rational Functions

Preparation

Runge's theorem

The Mittag-Leffler theorem

Simply connected regions

Exercises

Chapter 14 Conformal Mapping

Preservation of angles

Linear fractional transformations

Normal families

The Riemann mapping theorem

The class

Continuity at the boundary

Conformai mapping of an annulus

Exercises

Chapter 15 Zeros of Holomorphic Functions

Infinite products

The Weierstrass factorization theorem

An interpolation problem

Jensen's formula

Blaschke products

The Miintz-Szasz theorem

Exercises

Chapter 16 Analytic Continuation

Regular points and singular points

Continuation along curves

The monodromy theorem

Construction of a modular function

The Picard theorem

Exercises

Chapter 17 Hp-Spaces

Subharmonic functions

The spaces Hr and N

The theorem of F. and M. Riesz

Factorization theorems

The shift operator

Conjugate functions

Exercises

Chapter 18 Elementary Theory of Banach Algebras

Introduction

The invertible elements

Ideals and homomorphisms

Applications

Exercises

Chapter 19 Holomorphic Fourier Transforms

Introduction

Two theorems of Paley and Wiener

Quasi-analytic classes

The Denjoy-Carleman theorem

Exercises

Chapter 20 Uniform Approximation by Polynomials

Introduction

Some iemmas

Mergelyan's theorem

Exercises

Appendix: Hausdorff's Maximality Theorem

Notes and Comments

Bibliography

List of Special Symbols

Index

沃尔特·鲁丁（Walter Rudin） 1953年于杜克大学获得数学博士学位。曾先后执教于麻省理工学院、罗切斯特大学、威斯康星大学麦迪逊分校、耶鲁大学等。他的主要研究兴趣集中在调和分析和复变函数上。除本书外，他还著有《Functional Analysis》（泛函分析）和《Principles of Mathematical Analysis》（数学分析原理）等其他名著。这些教材已被翻译成十几种语言，在世界各地广泛使用。

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书籍介绍

本书是分析领域内的一部经典著作。主要内容包括：抽象积分、正博雷尔测度、LP-空间、希尔伯特空间的初等理论、巴拿赫空间技巧的例子、复测度、微分、积空间上的积分、傅里叶变换、全纯函数的初等性质、调和函数、最大模原理、有理函数逼近、共形映射、全纯函数的零点、解析延拓、HP-空间、巴拿赫代数的初等理论、全纯傅里叶变换、用多项式一致逼近等。另外，书中还附有大量设计巧妙的习题。本书体例优美，实用性很强，列举的实例简明精彩，基本上对所有给出的命题都进行了论证，适合作为高等院校数学专业高年级本科生和研究生的教材。