實分析（英文） [Real Analysis] pdf epub mobi txt 電子書 下載 2025

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[美] 斯坦恩（Stein E.M.） 著

齣版社： 世界圖書齣版公司

ISBN：9787510040535

版次：1

商品編碼：11142973

包裝：平裝

外文名稱：Real Analysis

開本：24開

齣版時間：2013-01-01

用紙：膠版紙

頁數：402

正文語種：英文

內容簡介

　　《實分析（英文）》在Princeton大學使用，同時在其它學校，比如UCLA等名校也在本科生教學中得到使用。其教學目的是，用統一的、聯係的觀點來把現代分析的“核心”內容教給本科生，力圖使本科生的分析學課程能接上現代數學研究的脈絡。

內頁插圖

目錄

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

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這書是給兒子買的，他說不錯，我看不懂

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好好好好好好好好好好好好

評分☆☆☆☆☆

看英文書就要看原版。

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英文原版，不錯的書!

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very good

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不愧為stein的經典著作，邏輯清晰，結構嚴謹，很棒

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這本書後麵印刷有很大問題，懷疑不是正版

評分☆☆☆☆☆

很好，是正品，就是沒時間看

評分☆☆☆☆☆

印刷質量不錯，比國外便宜很多