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。

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 projeCtions (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.  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 (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). Generalizations of Lusin's

      theorem (137). Metric outer measures (140). Capacities (142).

      Covariance operators and means of measures (142). The Choquet

      representation (145). Convolution (146). Measurable linear

      functions (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 transform

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. 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 (308). Extremal preimages of

      measures and uniqueness (310). Existence of atomless measures (317).

      Invariant and quasi-invariant measures of transformations (318). Point

      and Boolean isomorphisms (320). Almost homeomorphisms (323).

      Measures with given marginal projections (324). The Stone

      representation (325). The Lyapunov theorem (326). Exercises (329)

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 (398). Disintegrations (403). Strong liftings (406)

      Zero-one laws (407). Laws of large numbers (410). Gibbs

      measures (416). Triangular mappings (417). Exercises (427)

Bibliographical and Historical Comments

References

Author Index

Subject Index