Improper regular conditional distributions
type: Item
instance of: scholarly article
title: Improper regular conditional distributions
zbMATH Open document ID: 1017.60007
author: T. Seidenfeld
author: M. J. Schervish
author: Joseph B. Kadane
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: Let \((\Omega,\mathcal B,P)\) be a probability space and let \(\mathcal A\) be a conditioning sub-\(\sigma\)-field. An rcd (regular conditional distribution) \(P(.|\mathcal A)\) is said to be proper at \(\omega\in {\Omega}\) if \(P(A|{\mathcal A})(\omega)\) = 1 whenever \(\omega\in A\in {\mathcal A}\). If it is not everywhere proper, then it is said to be improper and if \(P(A|{\mathcal A})(\omega)\) = 0 for some \(\omega\in A\in {\mathcal A}\), then it is said to be maximally improper. In this rather technical paper, the authors explore the extent of local and global impropriety. Particular results deal with countably generated resp. symmetric sub-\(\sigma\)-fields. The concluding remarks are interesting.
reviewed by: Roman Frič
Mathematics Subject Classification ID: 60A10
zbMATH DE Number: 1906032
zbMATH Keywords: regular conditional distribution
zbMATH Keywords: conditioning sub-sigma-field
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1015345764
OpenAlex ID: W1998327739
cites work: Q4836494
cites work: Q3234851
cites work: On existence and non-existence of proper, regular, conditional distributions
cites work: Non-Existence of Everywhere Proper Conditional Distributions
cites work: Q5563135
cites work: Q5822308
cites work: Q5657452
cites work: Finitely additive conditional probabilities, conglomerability and disintegrations
cites work: Measurable, Tail Disintegrations of the Haar Integral are Purely Finitely Additive
cites work: Q5799972
cites work: Symmetric Measures on Cartesian Products
cites work: Q3756289
cites work: Q3238703
cites work: Q3226024
cites work: Q5826088
cites work: Theory of statistics
cites work: The extent of non-conglomerability of finitely additive probabilities
DOI: 10.1214/AOP/1015345764
description: scientific article; zbMATH DE number 1906032