A counterexample on the continuity of conditional expectations
type: Item
instance of: scholarly article
title: A counterexample on the continuity of conditional expectations
zbMATH Open document ID: 0641.60053
DOI: 10.1016/0022-247X(88)90229-6
author: Alberto Alonso
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: Martingae convergence theorems give the answers for some questions about the continuity of conditional expectations. This paper shows an example of a converging sequence (in a natural sense) of \(\sigma\)-algebras such that the corresponding sequence of conditional expectations does not converge a.e. The similar convergence in \(L^ p\) (1\(\leq p\leq \infty)\) holds (Fetter's theorem) and a simple proof of this theorem is given in this paper, too.
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 60F25
zbMATH DE Number: 4044870
zbMATH Keywords: Martingae convergence theorems
zbMATH Keywords: continuity of conditional expectations
MaRDI profile type: Publication
Wikidata QID: Q125038403
cites work: On the continuity of conditional expectations
cites work: Q5515914
cites work: Q5822308
cites work: Q3843987
description: scientific article; zbMATH DE number 4044870