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Princeton Lectures in Analysis系列中的第三本，Stein的力作。
Princeton Lectures in Analysis这套丛书，是作者们为普林斯顿大学本科生写的分析学系列教材，旨在对读过大学微积分以及线性代数的学生或科研工作者，提供一套分析学的核心教材。他们依次为：(I)傅立叶分析导论，(II)复分析，(III)实分析，(IV)泛函分析。第四本还没有出，如果需要我可以把前面两本一起传上来。从2000年起，普林斯顿大学的分析学就开始使用这套教材，而现在越来越多的北美高校开始采用这套教材。
就不多说了，需要的人自然知道这本书，不知道的google一下也就知道这套教材的影响了。下面是书的目录：
Elias M. Stein & Rami Shakarchi | 2005 | 392 pp.
TABLE OF CONTENTS:
Foreword vii
Introduction xv
Chapter 1. Measure Theory 1
1 Preliminaries 1
2 The exterior measure 10
3 Measurable sets and the Lebesgue measure 16
4 Measurable functions 7
5* The Brunn-Minkowski inequality 34
6 Exercises 37
7 Problems 46
Chapter 2: Integration Theory 49
1 The Lebesgue integral: basic properties and convergence theorems 49
2 Thespace L 1 of integrable functions 68
3 Fubini's theorem 75
4* A Fourier inversion formula 86
5 Exercises 89
6 Problems 95
Chapter 3: Differentiation and Integration 98
1 Differentiation of the integral 99
2 Good kernels and approximations to the identity 108
3 Differentiability of functions 114
4 Rectifiable curves and the isoperimetric inequality 134
5 Exercises 145
6 Problems 152
Chapter 4: Hilbert Spaces: An Introduction 156
1 The Hilbert space L 2 156
2 Hilbert spaces 161
3 Fourier series and Fatou's theorem 170
4 Closed subspaces and orthogonal projections 174
5 Linear transformations 180
6 Compact operators 188
7 Exercises 193
8 Problems 202
Chapter 5: Hilbert Spaces: Several Examples 207
1 The Fourier transform on L 2 207
2 The Hardy space of the upper half-plane 13
3 Constant coefficient partial differential equations 221
4* The Dirichlet principle 9
5 Exercises 253
6 Problems 259
Chapter 6: Abstract Measure and Integration Theory 262
1 Abstract measure spaces 263
2 Integration on a measure space 273
3 Examples 276
4 Absolute continuity of measures 285
5* Ergodic theorems 292
6* Appendix: the spectral theorem 306
7 Exercises 312
8 Problems 319
Chapter 7: Hausdorff Measure and Fractals 323
1 Hausdorff measure 324
2 Hausdorff dimension 329
3 Space-filling curves 349
4* Besicovitch sets and regularity 360
5 Exercises 380
6 Problems 385
Notes and References 389
Bibliography 391
Symbol Glossary 395
Index 397
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[此贴子已经被作者于2009-2-22 14:33:15编辑过]
mathtao 金币 +1 金钱 +100 魅力 +50 经验 +50 奖励 2009-4-23 22:30:10
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