Measures on topological spaces
type: Item
instance of: scholarly article
title: Measures on topological spaces
zbMATH Open document ID: 0910.28009
DOI: 10.1007/BF02432851
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-12-17T00:00:00Z
review text: This survey presents a complete, systematic and very well documented exposition of the integration theory on topological spaces. The central topics are: regularity, transformations and convergence of measures on topological spaces. It contains nine chapters. In Chapter 1, some set-theoretic preliminaries and topological concepts are given. In Chapter 2, various sigma-fields in topological spaces are introduced and the Souslin operation is defined. Chapter 3 deals with several regularity properties of measures, and Baire, Borel, Radon, and perfect measures are treated. Chapter 4 considers the regularity of measures in terms of functionals, and the Riesz-Markov theorems. Radon spaces (and related concepts) and the Skorohod topology are discussed in Chapter 5, while Chapter 6 is dedied to comment several questions about the transformations of measures, such as images of measures, invariant measures of transformations, liftings and conditional measures. Chapter 7 discusses the isomorphisms of measurable spaces and Chapter 8 presents an introduction to the convergence of measures. Here the main definitions and the most important results connected with weak convergence and weak compactness (including Prokhorov spaces), as well as numerous examples, are presented. Finally, Chapter 9 can be regarded as an introduction to the measure theory on topological linear spaces (and mainly on locally convex spaces). Some results are presented with complete proofs, in particular, this concerns a number of new results and examples. Furthermore, a list of 562 references is also given.
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 28-02
zbMATH DE Number: 1231429
zbMATH Keywords: measures
zbMATH Keywords: topological spaces
zbMATH Keywords: regular measures
zbMATH Keywords: image measure
zbMATH Keywords: convergence of measures
author: Vladimir I. Bogachev
reviewed by: P. Jiménez Guerra
MaRDI profile type: Publication
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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Measures on topological spaces (cites work)
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