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 ofSouslin
spaces (51). Measurability in normed spaces (52). TheSkorohod
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 offunctionals
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 andatomless
measures (133). Completion regular measures (133). Radon
spaces (135). Supports of measures (136). Generalizatio ofLusin'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 weaksequential
completeness of spaces of measures (226). The A-topology(226).
Continuous mappings of spaces of measures (227). Theseparability
of spaces of measures (230). Young measures (231). Metricson
spaces of measures (232). Uniformly distributed sequences(237).
Setwise convergence of measures (241). Stable convergenceand
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
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