测度论（第二卷）（影印版） / 天元基金影印数学丛书
￥45.10定价
作者： V.I.Bogachev
出版时间：2010年7月
出版社：高等教育出版社
- 高等教育出版社
- 9787040286977
- 1版
- 56781
- 0045150270-2
- 异16开
- 2010年7月
- 450
- 575
- 理学
- 数学
- O174.12
- 数学类
- 研究生、本科
内容简介
本书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，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，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
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 a-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 (43). Souslin setsas projeCtio
(46)./C-analytic
and F-analytic sets (49). Blackwell spaces (50). Mappings of
Souslin
spaces (51). Measurability in normed spaces (52). The
Skorohod
space (53). Exercises (54).
Chapter 7. Measures on topological spaces
7.1.Borel, Baire and Radon measures
7.2. T-additive measures
7.3. Exteio 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
Exteio of product measure (126). Measurability on products
(129).
Marfk spaces (130). Separable measures (132). Diffused and
atomless
measures (133). Completion regular measures (133). Radon
spaces (135). Supports of measures (136). Generalizatio of
Lusin's
theorem (137). Metric outer measures (140). Capacities
(142).
Covariance operato and mea of measures (142). The Choquet
representation (145). Convolution (146). Measurable linear
functio (149). Convex measures (149). Pointwise convergence
(151).
Infinite Radon measures (154). Exercises (155).
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 traform
8.9. Spaces of measures with the weak topology
8.10.Supplements and exercises
Weak compactness (217). Prohorov spaces (219). The weak
sequential
completeness of spaces of measures (226). The A-topology
(226).
Continuous mappings of spaces of measures (227). The
separability
of spaces of measures (230). Young measures (231). Metrics
on
spaces of measures (232). Uniformly distributed sequences
(237).
Setwise convergence of measures (241). Stable convergence
and
ws-topology (246). ,Exercises (249)
Chapter 9. Traformatio 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. Connectio with exteio 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 (308). Extremal preimages of
measures and uniqueness (310). Existence of atomless measures
(317).
Invariant and quasi-invariant measures of traformatio (318).
Point
and Boolean isomorphisms (320). Almost homeomorphisms
(323).
Measures with given marginal projectio (324). The Stone
representation (325). The Lyapunov theorem (326). Exercises
(329)
Chapter 10. Conditional measures and conditional
expectatio
10.1. Conditional expectatio
10.2. Convergence of conditional expectatio
10.3.Martingales
10.4.Regular conditional measures
10.5.Liftings and conditional measures
10.6. Disintegratio of measures
10.7.Traition measures
10.8.Measurable partitio
10.9.Ergodic theorems
10.10.Supplements and exercises
Independence (398). Disintegratio (403). Strong liftings
(406)
Zero-one laws (407). Laws of large numbe (410). Gibbs
measures (416). Triangular mappings (417). Exercises (427)
Bibliographical and Historical Comments
References
Author Index
Subject Index
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 a-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 (43). Souslin setsas projeCtio
(46)./C-analytic
and F-analytic sets (49). Blackwell spaces (50). Mappings of
Souslin
spaces (51). Measurability in normed spaces (52). The
Skorohod
space (53). Exercises (54).
Chapter 7. Measures on topological spaces
7.1.Borel, Baire and Radon measures
7.2. T-additive measures
7.3. Exteio 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
Exteio of product measure (126). Measurability on products
(129).
Marfk spaces (130). Separable measures (132). Diffused and
atomless
measures (133). Completion regular measures (133). Radon
spaces (135). Supports of measures (136). Generalizatio of
Lusin's
theorem (137). Metric outer measures (140). Capacities
(142).
Covariance operato and mea of measures (142). The Choquet
representation (145). Convolution (146). Measurable linear
functio (149). Convex measures (149). Pointwise convergence
(151).
Infinite Radon measures (154). Exercises (155).
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 traform
8.9. Spaces of measures with the weak topology
8.10.Supplements and exercises
Weak compactness (217). Prohorov spaces (219). The weak
sequential
completeness of spaces of measures (226). The A-topology
(226).
Continuous mappings of spaces of measures (227). The
separability
of spaces of measures (230). Young measures (231). Metrics
on
spaces of measures (232). Uniformly distributed sequences
(237).
Setwise convergence of measures (241). Stable convergence
and
ws-topology (246). ,Exercises (249)
Chapter 9. Traformatio 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. Connectio with exteio 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 (308). Extremal preimages of
measures and uniqueness (310). Existence of atomless measures
(317).
Invariant and quasi-invariant measures of traformatio (318).
Point
and Boolean isomorphisms (320). Almost homeomorphisms
(323).
Measures with given marginal projectio (324). The Stone
representation (325). The Lyapunov theorem (326). Exercises
(329)
Chapter 10. Conditional measures and conditional
expectatio
10.1. Conditional expectatio
10.2. Convergence of conditional expectatio
10.3.Martingales
10.4.Regular conditional measures
10.5.Liftings and conditional measures
10.6. Disintegratio of measures
10.7.Traition measures
10.8.Measurable partitio
10.9.Ergodic theorems
10.10.Supplements and exercises
Independence (398). Disintegratio (403). Strong liftings
(406)
Zero-one laws (407). Laws of large numbe (410). Gibbs
measures (416). Triangular mappings (417). Exercises (427)
Bibliographical and Historical Comments
References
Author Index
Subject Index
