Almost everywhere continuity of conditional expectations
Volume 11, Issue 3 (2024), pp. 247–263
Pub. online: 11 January 2024
Type: Research Article
Open Access
Open Access
Received
22 February 2023
22 February 2023
Revised
22 November 2023
22 November 2023
Accepted
25 November 2023
25 November 2023
Published
11 January 2024
11 January 2024
Abstract
A necessary and sufficient condition on a sequence ${\{{\mathcal{A}_{n}}\}_{n\in \mathbb{N}}}$ of σ-subalgebras which assures convergence almost everywhere of conditional expectations for functions in ${L^{\infty }}$ is given. It is proven that for $f\in {L^{\infty }}(\mathcal{A})$
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