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Measure theory(測度論) 版權(quán)信息
- ISBN：9787519224134
- 條形碼：9787519224134 ; 978-7-5192-2413-4
- 裝幀：一般膠版紙
- 冊數(shù)：暫無
- 重量：暫無
- 所屬分類：>>
Measure theory(測度論) 內(nèi)容簡介
《測度論（第2版 影印版 英文版）》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，并新增概率一章！稖y度論（第2版 影印版 英文版）》全面介紹了測度和積分，重在強調(diào)學習分析和測度必需的和相關(guān)的一些話題。前幾章講述了抽象測度和積分；后一章講述微分知識，包括Rd上變量的處理。每章末附有代表性的習題，從常規(guī)題型到擴展訓練都有涉及，較高難度的習題附有提示。
Measure theory(測度論) 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
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
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