測度論（第2版）

《測度論（第2版）》是2018年世界圖書出版公司出版的著作，作者是[美] D.L.科恩。

基本介紹

• 書名：《測度論（第2版）》
• 作者：[美] D.L.科恩
• 出版社：世界圖書出版公司
• 出版時間：2018年01月01日
• ISBN：9787519224134 

內容簡介

《測度論》是一部為初學者提供學習測度論的入門書籍，綜合性強，清晰易懂。本版與第1版相比，篇幅擴展100頁，並新增機率一章。全面介紹了測度和積分，重在強調學習分析和測度必需的和相關的一些話題。前五章講述了抽象測度和積分；第六章講述微分知識，包括Rd上變數的處理。每章末附有代表性的習題，從常規題型到擴展訓練都有涉及，較高難度的習題附有提示。

作者簡介

D.L.Cohn是美國Suffolk大學教授,本書的最大特點是初步並且全面的講述局部緊Hausdorff空間上的積分知識、Polish空間上的解析和Borel子集和局部緊群上的Haar測度，提供了調和分析和機率論的工具。

目錄

Introduction

1 Measures

1．1 Algebras and Sigma-Algebras

1．2 Measures

1．3 Outer Measures

1．4 Lebesgue Measure

1．5 Completeness and Regularity

1．6 Dynkin Classes

2 Functions and Integrals

2．1 Measurable Functions

2．2 Properties That Hold Almost Everywhere

2．3 The Integral

2．4 Limit Theorems

2．5 The Riemann Integral

2．6 Measurable Functions Again， Complex-Valued Functions， and Image Measures

3 Convergence

3．1 Modes of Convergence

3．2 Normed Spaces

3．3 Definition of LP and LP

3．4 Properties of LP and LP

3．5 Dual Spaces

4 Signed and Complex Measures

4．1 Signed and Complex Measures

4．2 Absolute Continuity

4．3 Singularity

4．4 Functions of Finite Variation

4．5 The Duals of the LP Spaces

5 Product Measures

5．1 Constructions

5．2 Fubini's Theorem

5．3 Applications

6 Differentiation

6．1 Change of Variable in Rd

6．2 Differentiation of Measures

6．3 Differentiation of Functions

7 Measures on Locally Compact Spaces

7．1 Locally Compact Spaces

7．2 The Riesz Representation Theorem

7．3 Signed and Complex Measures； Duality

7．4 Additional Properties of Regular Measures

7．5 The ?*-Measurable Sets and the Dual ofL1

7．6 Products of Locally Compact Spaces

7．7 The Daniell-Stone Integral

8 Polish Spaces and Analytic Sets

8．1 Polish Spaces

8．2 Analytic Sets

8．3 The Separation Theorem and Its Consequences

8．4 The Measurability of Analytic Sets

8．5 Cross Sections

8．6 Standard， Analytic， Lusin， and Souslin Spaces

9 Haar Measure

9．1 Topological Groups

9．2 The Existence and Uniqueness of Haar Measure

9．3 Properties of Haar Measure

9．4 The Algebras L1 （G） and M（G）

10 Probability

10．1 Basics

10．2 Laws of Large Numbers

10．3 Convergence in Distribution and the Central Limit Theorem

10．4 Conditional Distributions and Martingales

10．5 Brownian Motion

10．6 Construction of Probability Measures

ANotation and Set Theory

BAlgebra and Basic Facts About R and C

CCalculus and Topology in Rd

DTopological Spaces and Metric Spaces

EThe Bochner Integral

FLiftings

GThe Banach-Tarski Paradox

HThe Henstock-Kurzweii and McShane Integrals

References

Index of notation

Index