This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.
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Constructions and extensions of measures.- The Lebesgue integral.- Operations on measures and functions.- The spaces Lp and spaces of measures.- Connections between the integral and derivative.- Borel, Baire and Souslin sets.- Measures on topological spaces.- Weak convergence of measure.- Transformations of measures and isomorphisms.- Conditional measures and conditional.Giới thiệu về tác giả
Vladimir Bogachev was born in Moscow in 1961. He got the Ph D 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.
Ngôn ngữ Anh ● định dạng PDF ● Trang 1075 ● ISBN 9783540345145 ● Kích thước tập tin 10.3 MB ● Nhà xuất bản Springer Berlin ● Thành phố Heidelberg ● Quốc gia DE ● Được phát hành 2007 ● Có thể tải xuống 24 tháng ● Tiền tệ EUR ● TÔI 2162084 ● Sao chép bảo vệ DRM xã hội
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