Real Analysis/Stein Shakarchi 实分析 斯坦恩 英文版

　　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。
8 E, ]7 I: s- w9 a, Z, c　　作者简介
6 A( j* w4 ^  t* ^- s" T　　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
9 G" m' n8 p8 P　　5 The problem of measure
　　Chapter 1. Measure Theory
" @2 Q/ V# i6 F: M3 G% K6 R　　1 Preliminaries
9 _7 }7 i2 ^# G. Q* d　　2 The exterior measure
% H- }4 U' {' _; C2 U( t; I) F　　3 Measurable sets and the Lebesgue measure4 Measurable functions
4 L+ v$ n$ @3 U8 _　　4.1 Definition and basic properties
! X$ N7 l: K7 V　　4.2 Approximation by simple functions or step functions4.3 Littlewood's three principles
  X9 Q+ `# ^9 _% M) T6 I　　5* The Brunn-Minkowski inequality
9 O6 ]" w' M2 S: K' `9 {8 D0 l　　6 Exercises
% }# B! \5 y! R2 D( R　　7 Problems
　　Chapter 2. Integration Theory
! B: b% b& B" P, A! a　　1 The Lebesgue integral: basic properties and convergence theorems2 The space L1 of integrable functions
' M. g5 ^# x, L3 c　　3 Fubini's theorem
2 [  T$ [( e! x- P　　3.1 Statement and proof of the theorem
　　3.2 Applications of Fubini's theorem
　　4* A Fourier inversion formula
　　5 Exercises
$ n$ g; }+ }% x8 {' r　　6 Problems
5 M6 V% Z; X7 j0 _0 C　　Chapter 3. Differentiation and Integration1 Differentiation of the integral
　　1.1 The Hardy-Littlewood maximal function1.2 The Lebesgue differentiation theorem
. W. [' V: a  w. E6 h　　2 Good kernels and approximations to the identity3 Differentiability of functions
　　3.1 Functions of bounded variation
, f( `0 q9 J' j5 s7 S　　3.2 Absolutely continuous functions
' ?1 `5 F% L* s5 h" F# a9 z　　3.3 Differentiability of jump functions
* L4 {: ~- b/ L% w* P; x　　4 Rectifiable curves and the isoperimetric inequality4.1 Minkowski content of a curve
　　4.2* Isoperimetrie inequality
- a; T3 m0 I7 }2 V* _　　5 Exercises
% [0 q& z" M! r$ Q　　6 Problems
　　Chapter 4. Hilbert Spaces: An Introduction1 The Hilbert space L2
# N4 `! E$ Y1 X9 q" Q+ m9 M( y　　2 Hilbert spaces
　　2.1 Orthogonality
　　2.2 Unitary mappings
1 @, f7 N% @3 }: Q4 l  C5 c　　2.3 Pre-Hilbert spaces
+ i& Y) A8 \( r  x( k' E" I　　3 Fourier series and Fatou's theorem
　　3.1 Fatou's theorem
% R3 Q; o' A6 L, \　　4 Closed subspaees and orthogonal projections5 Linear transformations
* G) {; L8 g# g% e9 s. I& z　　5.1 Linear flmetionals and the Riesz representation the-orem5.2 Adjoints
　　5.3 Examples
　　6 Compact operators
" D/ M1 V. n! B' W! f　　7 Exercises
# o. n9 q) N2 h: n8 P" U　　8 Problems
　　Chapter 5. Hilbert Spaces: Several Examples1 The Fourier transform on L2
  `$ f0 P, f/ `! W% U: N　　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
' u7 s, q6 `; Q" E; d9 W# d　　Notes and References
+ ^! S9 q2 M7 X. p　　Bibliography
　　Symbol Glossary
/ I* X8 \# j3 o. y9 A& m　　Index

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