On semiregular conditional distributions

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1992 English Publisher:Springer Science and Business Media LLCJournal:Journal of Theoretical Probability, volume 5, pages 577-584 (issn: 0894-9840, eissn: 1572-9230,

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Authors: Plachky, D.;

doi: 10.1007/bf01060437

On semiregular conditional distributions

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Abstract

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.

Related Organizations

University of Münster
Germany

Keywords

Probabilistic measure theory, lifting, semiregular conditional distributions

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