Measure Theory (eBook)

Vladimir Bogachev was born in Moscow in 1961. He got the PhD at Moscow State University in 1986 and he got the degree of Doctor of Sciences in 1990. Since 1986 Vladimir Bogachev has worked at the Department of Mechanics and Mathematics of Moscow State University. The main fields of his research are measure theory, nonlinear functional analysis, probability theory, and stochastic analysis. He is a well-nown expert in measure theory, probability theory, and the Malliavin calculus, and the author of more than 100 scientific publications. His monograph ``Gaussian Measures’’ (AMS, 1998) has become a widely used source. Vladimir Bogachev hs been an invited speaker and a lecturer at many international conferences and several dozen universities and mathematical institutes over the world. Scientific awards: a medal of the Academy of Sciences of the USSR and the Award of the Japan Society of Promotion of Science.

Preface 5
Contents 11
Contents of Volume 2 14
Constructions and extensions of measures 17
The Lebesgue integral 121
Operations on measures and functions 191
The spaces Lp and spaces of measures 265
Connections between the integral and 345
Connections between the integral and derivative 345
Bibliographical and Historical Comments 425
References 456
Subject Index 506
Preface to Volume 2 519
Contents 521
Contents of Volume 1 524
Borel, Baire and Souslin sets 527
Measures on topological spaces 593
Weak convergence of measures 701
Transformations of measures and isomorphisms 793
Conditional measures and conditional expectations 865
Bibliographical and Historical Comments 965
References 991
Subject Index 1087