测度论（第2卷）（影印版）
目 录内容简介
Preface to Volume 2
Chapter 6 Borel， Baire and Souslin sets
6.1.Metric and topological spaces
6.2.Borel sets
6.3.Baire sets
6.4.Products of topological spaces
6.5.Countably generated σ-algebras
6.6.Souslin sets and their separation
6.7.Sets in Souslin spaces
6.8.Mappings of Souslin spaces
查看完整
Chapter 6 Borel， Baire and Souslin sets
6.1.Metric and topological spaces
6.2.Borel sets
6.3.Baire sets
6.4.Products of topological spaces
6.5.Countably generated σ-algebras
6.6.Souslin sets and their separation
6.7.Sets in Souslin spaces
6.8.Mappings of Souslin spaces
查看完整
目 录内容简介
《测度论（第2卷）（影印版）》是作者在莫斯科国立大学数学力学系的讲稿基础上编写而成的。第二卷介绍测度论的专题性的内容，特别是与概率论和点集拓扑有关的课题：Borel集，Baire集，Souslin集，拓扑空间上的测度，Kolmogorov定理，Daniell积分，测度的弱收敛，Skorohod表示，Prohorov定理，测度空间上的弱拓扑，Lebesgue-Rohlin空间，Haar测度，条件测度与条件期望，遍历理论等。每章最后都附有非常丰富的补充与练习，其中包含许多有用的知识，例如：Skorohod空间，Blackwell空间，Marik空间，Radon空间，推广的Lusin定理，容量，Choquet表示，Prohorov空间，Young测度等。书的最后有详尽的参考文献及历史注记。这是一本很好的研究生教材和教学参考书。
目 录内容简介
Preface to Volume 2
Chapter 6 Borel， Baire and Souslin sets
6.1.Metric and topological spaces
6.2.Borel sets
6.3.Baire sets
6.4.Products of topological spaces
6.5.Countably generated σ-algebras
6.6.Souslin sets and their separation
6.7.Sets in Souslin spaces
6.8.Mappings of Souslin spaces
6.9.Measurable choice theorems
6.10.Supplements and exercises
Borel and Baire sets
Souslin sets as projections
K-analytic and F-analytic sets
Blackwell spaces
Mappings of Souslin spaces
Measurability in normed spaces
The Skorohod space
Exercises
Chapter 7 Measures on topological spaces
7.1.Borel， Baire and Radon measures
7.2.τ-additive measures
7.3.Extensions of measures
7.4.Measures on Souslin spaces
7.5.Perfect measures
7.6.Products of measures
7.7.The Kolmogorov theorem
7.8.The Daniell integral
7.9.Measures as functionals
7.10.The regularity of measures in terms of functionals
7.11.Measures on locally compact spaces
7.12.Measures on linear spaces
7.13.Characteristic functionals
7.14.Supplements and exercises
Extensions of product measure
Measurability on products
Marik spaces
Separable measures
Diffused and atomless measures
Completion regular measures
Radon spaces
Supports of measures
Generalizations of Lusins theorem
Metric outer measures
Capacities
Covariance operators and means of measures
The Choquet representation
Convolution
Measurable linear functions
Convex measures
Pointwise convergence
Infinite Radon measures
Exercises
Chapter 8 Weak convergence of measures
8.1.The definition of weak convergence
8.2.Weak convergence of nonnegative measures
8.3.The case of a metric space
8.4.Some properties of weak convergence
8.5.The Skorohod representation
8.6.Weak compactness and the Prohorov theorem
8.7.Weak sequential completeness
8.8.Weak convergence and the Fourier transform
8.9.Spaces of measures with the weak topology
8.10.Supplements and exercises
Weak compactness
Prohorov spaces
The weak sequential completeness of spaces of measures
The A-topology
Continuous mappings of spaces of measures
The separability of spaces of measures
Young measures
Metrics on spaces of measures
Uniformly distributed sequences
Setwise convergence of measures
Stable convergence and ws-topology
Exercises
Chapter 9 Transformations of measures and isomorphisms
9.1.Images and preimages of measures
9.2.Isomorphisms of measure spaces
9.3.Isomorphisms of measure algebras
9.4.Lebesgue-Rohlin spaces
9.5.Induced point isomorphisms
9.6.Topologically equivalent measures
9.7.Continuous images of Lebesgue measure
9.8.Connections with extensions of measures
9.9.Absolute continuity of the images of measures
9.10.Shifts of measures along integral curves
9.11.Invariant measures and Haar measures
9.12.Supplements and exercises
Projective systems of measures
Extremal preimages of measures and uniqueness
Existence of atomlees measures
Invariant and quasi-invariant measures of transformations
Point and Boolean isomorphisms
Almost homeomorphisms Measures with given marginal projections
The Stonerepresentation
The Lyapunov theorem
Exercises
Chapter 10 Conditional measures and conditional expectations
10.1.Conditional expectations
10.2.Convergence of conditional expectations
10.3.Martingales
10.4.Regular conditional measures
10.5.Liftings and conditional measures
10.6.Disintegrations of measures
10.7.Transition measures
10.8.Measurable partitions
10.9.Ergodic theorems
10.10.Supplements and exercises
Independence
Disintegrations
Strong liftings
Zero-one laws
Laws of large numbers
Gibbs measures
Triangular mappings
Exercises
Bibliographical and Historical Comments
References
Author Index
Subject Index
^ 收 起
Chapter 6 Borel， Baire and Souslin sets
6.1.Metric and topological spaces
6.2.Borel sets
6.3.Baire sets
6.4.Products of topological spaces
6.5.Countably generated σ-algebras
6.6.Souslin sets and their separation
6.7.Sets in Souslin spaces
6.8.Mappings of Souslin spaces
6.9.Measurable choice theorems
6.10.Supplements and exercises
Borel and Baire sets
Souslin sets as projections
K-analytic and F-analytic sets
Blackwell spaces
Mappings of Souslin spaces
Measurability in normed spaces
The Skorohod space
Exercises
Chapter 7 Measures on topological spaces
7.1.Borel， Baire and Radon measures
7.2.τ-additive measures
7.3.Extensions of measures
7.4.Measures on Souslin spaces
7.5.Perfect measures
7.6.Products of measures
7.7.The Kolmogorov theorem
7.8.The Daniell integral
7.9.Measures as functionals
7.10.The regularity of measures in terms of functionals
7.11.Measures on locally compact spaces
7.12.Measures on linear spaces
7.13.Characteristic functionals
7.14.Supplements and exercises
Extensions of product measure
Measurability on products
Marik spaces
Separable measures
Diffused and atomless measures
Completion regular measures
Radon spaces
Supports of measures
Generalizations of Lusins theorem
Metric outer measures
Capacities
Covariance operators and means of measures
The Choquet representation
Convolution
Measurable linear functions
Convex measures
Pointwise convergence
Infinite Radon measures
Exercises
Chapter 8 Weak convergence of measures
8.1.The definition of weak convergence
8.2.Weak convergence of nonnegative measures
8.3.The case of a metric space
8.4.Some properties of weak convergence
8.5.The Skorohod representation
8.6.Weak compactness and the Prohorov theorem
8.7.Weak sequential completeness
8.8.Weak convergence and the Fourier transform
8.9.Spaces of measures with the weak topology
8.10.Supplements and exercises
Weak compactness
Prohorov spaces
The weak sequential completeness of spaces of measures
The A-topology
Continuous mappings of spaces of measures
The separability of spaces of measures
Young measures
Metrics on spaces of measures
Uniformly distributed sequences
Setwise convergence of measures
Stable convergence and ws-topology
Exercises
Chapter 9 Transformations of measures and isomorphisms
9.1.Images and preimages of measures
9.2.Isomorphisms of measure spaces
9.3.Isomorphisms of measure algebras
9.4.Lebesgue-Rohlin spaces
9.5.Induced point isomorphisms
9.6.Topologically equivalent measures
9.7.Continuous images of Lebesgue measure
9.8.Connections with extensions of measures
9.9.Absolute continuity of the images of measures
9.10.Shifts of measures along integral curves
9.11.Invariant measures and Haar measures
9.12.Supplements and exercises
Projective systems of measures
Extremal preimages of measures and uniqueness
Existence of atomlees measures
Invariant and quasi-invariant measures of transformations
Point and Boolean isomorphisms
Almost homeomorphisms Measures with given marginal projections
The Stonerepresentation
The Lyapunov theorem
Exercises
Chapter 10 Conditional measures and conditional expectations
10.1.Conditional expectations
10.2.Convergence of conditional expectations
10.3.Martingales
10.4.Regular conditional measures
10.5.Liftings and conditional measures
10.6.Disintegrations of measures
10.7.Transition measures
10.8.Measurable partitions
10.9.Ergodic theorems
10.10.Supplements and exercises
Independence
Disintegrations
Strong liftings
Zero-one laws
Laws of large numbers
Gibbs measures
Triangular mappings
Exercises
Bibliographical and Historical Comments
References
Author Index
Subject Index
^ 收 起
目 录内容简介
《测度论（第2卷）（影印版）》是作者在莫斯科国立大学数学力学系的讲稿基础上编写而成的。第二卷介绍测度论的专题性的内容，特别是与概率论和点集拓扑有关的课题：Borel集，Baire集，Souslin集，拓扑空间上的测度，Kolmogorov定理，Daniell积分，测度的弱收敛，Skorohod表示，Prohorov定理，测度空间上的弱拓扑，Lebesgue-Rohlin空间，Haar测度，条件测度与条件期望，遍历理论等。每章最后都附有非常丰富的补充与练习，其中包含许多有用的知识，例如：Skorohod空间，Blackwell空间，Marik空间，Radon空间，推广的Lusin定理，容量，Choquet表示，Prohorov空间，Young测度等。书的最后有详尽的参考文献及历史注记。这是一本很好的研究生教材和教学参考书。
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