Continuity of conditional expectation in Orlicz spaces

Abstract

The continuity of conditional expectation on Orlicz spaces is investigated. Indeed, we provide some necessary and sufficient conditions on a sequence $\{{\mathcal{A}}_n{\}}_{n\in \mathbb{N}}$ of $\ddot{I}ƒ$-subalgebras for $L^{\ddot{I}}†$-convergence of the related conditional expectations. Our results generalize similar results in $L^p$-spaces.

20 pages