实分析（英文） [Real Analysis] epub pdf mobi txt 电子书 下载 2024

实分析（英文） [Real Analysis] epub pdf mobi txt 电子书 下载 2024

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实分析（英文） [Real Analysis] epub pdf mobi txt 电子书 下载 2024

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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。

内页插图

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

实分析（英文） [Real Analysis] epub pdf mobi txt 电子书 下载 2024

实分析（英文） [Real Analysis] 下载 epub mobi pdf txt 电子书 2024

评分☆☆☆☆☆

stein四部分析曲之一，经典不容错过。

评分☆☆☆☆☆

经典书籍，没来得及看呢，先赞一个

评分☆☆☆☆☆

很好，是正品，就是没时间看

评分☆☆☆☆☆

印刷质量很好，知识系统，参考价值大，大师作品就是不一样。

评分☆☆☆☆☆

一年生蔓生藤本；茎、枝粗壮，具明显的棱沟。卷须较粗壮，具短柔毛，叶柄粗，密被柔毛；叶片纸质，轮廓三角状卵形，带白绿色，两面具短硬毛，叶片基部心形。雌雄同株。雌、雄花均单生于叶腋。雄花花梗长3-4厘米，密被黄褐色长柔毛；花萼筒宽钟形；花冠淡黄色；雄蕊近离生，花丝短，药室折曲。雌花：花萼和花冠与雄花同；子房卵形，柱头肾形。果实大型，近于球形或椭圆形，肉质，多汁，果皮光滑，色泽及纹饰各式。种子多数，卵形，黑色、红色，两面平滑，基部钝圆，通常边缘稍拱起，花果期夏季

评分☆☆☆☆☆

好评

评分☆☆☆☆☆

高级实分析教程，适合高年级学生使用。

评分☆☆☆☆☆

给男朋友买的，想凑四本，结果傅立叶分析没货，其他都很不错

评分☆☆☆☆☆

经典的教材，京东活动时购买的，很喜欢。

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