03940nam a22005295i 4500 978-3-540-34514-5 DE-He213 20210615111528.0 cr nn 008mamaa 100301s2007 gw | s |||| 0|eng d 9783540345145 978-3-540-34514-5 10.1007/978-3-540-34514-5 doi QA299.6-433 PBK bicssc MAT034000 bisacsh PBK thema 515 23 Bogachev, Vladimir I. author. aut http://id.loc.gov/vocabulary/relators/aut Measure Theory [electronic resource] / by Vladimir I. Bogachev. 1st ed. 2007. Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2007. XVII, 1075 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. Measure theory is a classical area of mathematics that continues intensive development and has fruitful connections with most other fields of mathematics as well as important applications in physics. This book gives a systematic presentation of modern measure theory as it has developed over the past century and offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course (the material of this level corresponds to a variety of special courses), and, finally, more specialized topics partly covered by more than 850 exercises. Bibliographical and historical comments and an extensive bibliography with 2000 works covering more than a century are provided. Volume 1 is devoted to the classical theory of measure and integral. Whereas the first volume presents the ideas that go back mainly to Lebesgue, the second volume is to a large extent the result of the later development up to the recent years. The central subjects of Volume 2 are: transformations of measures, conditional measures, and weak convergence of measures. These topics are closely interwoven and form the heart of modern measure theory. The target readership includes graduate students interested in deeper knowledge of measure theory, instructors of courses in measure and integration theory, and researchers in all fields of mathematics. The book may serve as a source for many advanced courses or as a reference. Mathematical analysis. Analysis (Mathematics). Measure theory. Functional analysis. Probabilities. Analysis. https://scigraph.springernature.com/ontologies/product-market-codes/M12007 Measure and Integration. https://scigraph.springernature.com/ontologies/product-market-codes/M12120 Functional Analysis. https://scigraph.springernature.com/ontologies/product-market-codes/M12066 Probability Theory and Stochastic Processes. https://scigraph.springernature.com/ontologies/product-market-codes/M27004 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783540824640 Printed edition: 9783540345138 Printed edition: 9783662500705 https://doi.org/10.1007/978-3-540-34514-5 ZDB-2-SMA ZDB-2-SXMS Mathematics and Statistics (SpringerNature-11649) Mathematics and Statistics (R0) (SpringerNature-43713)