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
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