实分析（英文） [Real Analysis] pdf epub mobi txt 电子书 下载 2025

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[美] 斯坦恩（Stein E.M.） 著

出版社： 世界图书出版公司

ISBN：9787510040535

版次：1

商品编码：11142973

包装：平装

外文名称：Real Analysis

开本：24开

出版时间：2013-01-01

用纸：胶版纸

页数：402

正文语种：英文

内容简介

　　《实分析（英文）》在Princeton大学使用，同时在其它学校，比如UCLA等名校也在本科生教学中得到使用。其教学目的是，用统一的、联系的观点来把现代分析的“核心”内容教给本科生，力图使本科生的分析学课程能接上现代数学研究的脉络。

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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 Prelhninaries
2 The exterior measure
3 Measurable sets and the Lebesgue measure
4 Measurable functions
4.1 Definition and basic properties
4.2 Approximation by simple functions or step functions
4.3 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 theorems
2 The space L1 ofintegrable 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 Integration
1 Differentiation of the integral
1.1 The Hardy-Littlewood maximal function
1.2 The Lebesgue differentiation theorem
2 Good kernels and approximations to the identity
3 Differentiability of functions
3.1 Functions of bounded variation
3.2 Absolutely continuous functions
3.3 Differentiability ofjump functions
4 Rectifiable curves and the isoperimetric inequality
4.1 Minkowski content of a curve
4.2 Isoperimetric inequality
5 Exercises
6 Problems

Chapter 4. Hilbert Spaces： An Introduction
1 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 subspaces and orthogonal projections
5 Linear transformations
5.1 Linear functionals and the Riesz representation theorem
5.2 Adjoints
5.3 Examples
6 Compact operators
7 Exercises
8 Problems

Chapter 5. Hilbert Spaces： Several Examples
1 The Fourier transform on L2
2 The Hardy space of the upper half-plane
3 Constant coefficient partial differential equations
3.1 Weaak solutions
3.2 The main theorem and key estimate
4 The Dirichlet principle
4.1 Harmonic functions
4.2 The boundary value problem and Dirichlet's principle
5 Exercises
6 Problems

Chapter 6. Abstract Measure and Integration Theory
Chapter 7. Hausdorff Measure and Fractals
Notes and References
Bibliography
Symbol Glossary
Index

前言/序言

评分☆☆☆☆☆

经典好书，有点小贵，以前电子版打印了的，半价活动就入手了

评分☆☆☆☆☆

大师之作，值得一读，尤其数学系的学生更应该认真学学

评分☆☆☆☆☆

专业书籍，活动价格较为实惠，送货快。

评分☆☆☆☆☆

看英文书就要看原版。

评分☆☆☆☆☆

包装很好 送货也很快。

评分☆☆☆☆☆

书很不错只是物流希望更小心。

评分☆☆☆☆☆

实分析这本书很好～看目录就知道主要是讲测度等知识～我很喜欢这个作者～才买这书的！斯坦是个大师级人物，虽然我学识较浅，但是有时间可以看看，这书挺好的！就是比较难而已！都研究生了～得慢慢研究～哈哈……

评分☆☆☆☆☆

物流速度很快，书质量很好！

评分☆☆☆☆☆

书角烂了