Functors of probability measures in topological categories
type: Item
instance of: scholarly article
title: Functors of probability measures in topological categories
zbMATH Open document ID: 0944.28010
DOI: 10.1007/BF02432852
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-12-20T00:00:00Z
review text: The work represents a detailed survey of topological properties of probability measure spaces and their maps. It is organized as follows. Section 1 deals with preliminaries and the proof of normality of the functor \(P\) of probability measures in the category \(Comp\) of compacts. Section 2 is devoted to general properties of the functors \(P_\beta , P_r, P_\tau,\) where \(P_\beta (X)\) is the space of probability measures on \(X\) with compact supports, \(P_r\)(X) is the space of Radon probability measures on \(X\) , while \(P_\tau (X)\) is the space of \(\tau\)-smooth probability measures on \(X\). In Section 3 the author gives constructions permitting to lift the functor \(P_\beta\) to the categories \(Metr_b\) of bounded metric spaces and \(Metr_{bu}\) of bounded metric spaces and uniformly continuous mappings. In Section 4 results of Section 3 are used to lift the functor \(P_\beta\) to the category \(Unif\) of uniform spaces. Section 5 contains many results with detailed proofs. Among them is the author's theorem characterizing Tychonoff bundles in the class of mappings of the form \(P(f)\). Section 6 deals with the mapping of barycenter. Section 7 contains a survey of new results.
reviewed by: S. A. Chobanjan
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 28A33
zbMATH DE Number: 1231430
zbMATH Keywords: functors of probability measures
zbMATH Keywords: topological categories
zbMATH Keywords: category of bounded metric spaces
zbMATH Keywords: category of uniform spaces
zbMATH Keywords: Tychonoff bundle
author: V. V. Fedorchuk
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02432852
OpenAlex ID: W1971133420
description: scientific article; zbMATH DE number 1231430