On semiregular conditional distributions
type: Item
instance of: scholarly article
title: On semiregular conditional distributions
zbMATH Open document ID: 0761.60004
DOI: 10.1007/BF01060437
published in: Journal of Theoretical Probability
publication date: 1992-09-27T00:00:00Z
review text: Let \((\Omega,{\mathcal A},P)\) denote some probability space and \(\mathcal B\) some sub-\(\sigma\)-algebra of \(\mathcal A\). The existence of a semiregular version of \(P(A|{\mathcal B})\) is studied using a lifting \(L_ 1(\Omega,{\mathcal B},P|{\mathcal B})\to B(\Omega)\). \(B\) is the set of all real bounded functions on \(\Omega\). A strongly semiregular version of \(P(A|{\mathcal B})\) exists if \(L_ 1(\Omega,{\mathcal A},P)\) is separable. The possible decompositions of \(P\) are also formulated.
Mathematics Subject Classification ID: 60A10
zbMATH DE Number: 64460
zbMATH Keywords: semiregular conditional distributions
zbMATH Keywords: lifting
author: Detlef Plachky
reviewed by: Pavel Froněk
MaRDI profile type: Publication
cites work: Q3254057
cites work: Extremal and Monogenic Additive Set Functions
full work available at URL: https://doi.org/10.1007/bf01060437
OpenAlex ID: W2086642002
description: scientific article; zbMATH DE number 64460