Combinatorial methods in the study of marginal problems over separable spaces
type: Item
instance of: scholarly article
title: Combinatorial methods in the study of marginal problems over separable spaces
zbMATH Open document ID: 0523.60007
DOI: 10.1016/0022-247X(83)90208-1
author: R. M. Shortt
published in: Journal of Mathematical Analysis and Applications
publication date: 1983-01-01T00:00:00Z
review text: The paper deals with multidimensional (infinite) forms of the following question: When has a triple of separable spaces \(X,Y,Z\) the property that to any Borel probability measure \(P\) on \(X\times Y\) and \(Q\) on \(Y\times Z\) one can finda measure \(R\) on \(X\times Y\times Z\) with the marginals \(P,Q\). In the second part of the paper the question is extended to the case of projective systems of spaces. A basic property of the underlying spaces is the property that each probability measure is tight, which is called 'universally measurable' in this paper. The construction is based on the analysis of the combinatorial structure of the set of marginals (simplicial complexes) as introduced in the case of finite sets by \textit{N. N. Vorob'ev}, Consistent families of measures and their extensions. Teor. Veroyatn. Primen. 7, 153-169 (1962).
Mathematics Subject Classification ID: 60A10
Mathematics Subject Classification ID: 28A35
zbMATH DE Number: 3828925
zbMATH Keywords: product marginal system
zbMATH Keywords: combinatorial properties
zbMATH Keywords: Kolmogoroff consistency theorems
zbMATH Keywords: projective limits
MaRDI profile type: Publication
cites work: Approximation theorems for independent and weakly dependent random vectors
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cites work: Almost sure invariance principles for partial sums of weakly dependent random variables
cites work: Strassen's marginal problem in two or more dimensions
cites work: Q5600508
cites work: Markov Measures and Markov Extensions
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description: scientific article; zbMATH DE number 3828925