《測度論（第2卷）（影印版）》是作者在莫斯科國立大學(xué)數(shù)學(xué)力學(xué)系的講稿基礎(chǔ)上編寫而成的。第二卷介紹測度論的專題性的內(nèi)容，特別是與概率論和點(diǎn)集拓?fù)溆嘘P(guān)的課題：Borel集，Baire集，Souslin集，拓?fù)淇臻g上的測度，Kolmogorov定理，Daniell積分，測度的弱收斂，Skorohod表示，Prohorov定理，測度空間上的弱拓?fù)�，Lebesgue-Rohlin空間，Haar測度，條件測度與條件期望，遍歷理論等。每章最后都附有非常豐富的補(bǔ)充與練習(xí)，其中包含許多有用的知識，例如：Skorohod空間，Blackwell空間，Marik空間，Radon空間，推廣的Lusin定理，容量，Choquet表示，Prohorov空間，Young測度等。書的最后有詳盡的參考文獻(xiàn)及歷史注記。這是一本很好的研究生教材和教學(xué)參考書。
為了更好地借鑒國外數(shù)學(xué)教育與研究的成功經(jīng)驗(yàn)，促進(jìn)我國數(shù)學(xué)教育與研究事業(yè)的發(fā)展，提高高等學(xué)校數(shù)學(xué)教育教學(xué)質(zhì)量，本著“為我國熱愛數(shù)學(xué)的青年創(chuàng)造一個較好的學(xué)習(xí)數(shù)學(xué)的環(huán)境”這一宗旨，天元基金贊助出版“天元基金影印數(shù)學(xué)叢書”。
該叢書主要包含國外反映近代數(shù)學(xué)發(fā)展的純數(shù)學(xué)與應(yīng)用數(shù)學(xué)方面的優(yōu)秀書籍，天元基金邀請國內(nèi)各個方向的知名數(shù)學(xué)家參與選題的工作，經(jīng)專家遴選、推薦，由高等教育出版社影印出版。為了提高我國數(shù)學(xué)研究生教學(xué)的水平，暫把選書的目標(biāo)確定在研究生教材上。當(dāng)然，有的書也可作為高年級本科生教材或參考書，有的書則介于研究生教材與專著之間。
歡迎各方專家、讀者對本叢書的選題、印刷、銷售等工作提出批評和建議。
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
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