作者：D.L.科恩
页数：457
出版社：世界图书出版公司
出版日期：2017
ISBN：9787519224134
电子书格式：pdf/epub/txt
内容简介
《测度论》是一部为初学者提供学习测度论的入门书籍，综合性强，清晰易懂。本版与第1版相比，篇幅扩展100页，并新增概率一章。全面介绍了测度和积分，重在强调学习分析和测度必需的和相关的一些话题。前五章讲述了抽象测度和积分；第六章讲述微分知识，包括Rd上变量的处理。每章末附有代表性的习题，从常规题型到扩展训练都有涉及，较高难度的习题附有提示。
作者简介
D.L.Cohn是美国Suffolk大学教授,本书的最大特点是初步并且全面的讲述局部紧Hausdorff空间上的积分知识、Polish空间上的解析和Borel子集和局部紧群上的Haar测度，提供了调和分析和概率论的工具。
本书特色
《测度论》是一部为初学者提供学习测度论的入门书籍，综合性强，清晰易懂。本版与第1版相比，篇幅扩展100页，并新增概率一章。全面介绍了测度和积分，重在强调学习分析和测度必需的和相关的一些话题。前五章讲述了抽象测度和积分；第六章讲述微分知识，包括Rd上变量的处理。每章末附有代表性的习题，从常规题型到扩展训练都有涉及，较高难度的习题附有提示。
目录
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 μ最-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
A Notation and Set Theory
B Algebra and Basic Facts About R and C
C Calculus and Topology in Rd
D Topological Spaces and Metric Spaces
E The Bochner Integral
F Liftings
G The Banach-Tarski Paradox
H The Henstock-Kurzweii and McShane Integrals
References
Index of notation
Index
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 μ最-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
A Notation and Set Theory
B Algebra and Basic Facts About R and C
C Calculus and Topology in Rd
D Topological Spaces and Metric Spaces
E The Bochner Integral
F Liftings
G The Banach-Tarski Paradox
H The Henstock-Kurzweii and McShane Integrals
References
Index of notation
Index
