Abstract:In this paper we prove two convergence theorems for set-valued conditional expectations. The first is a set-valued generalization of Levy's martingale convergence theorem, while the second involves a nonmonotone sequence of sub $\sigma $-fields.
Keywords: measurable multifunction, set-valued conditional expectation, Levy's theorem, support function, Kuratowski-Mosco convergence of sets
AMS Subject Classification: 60D05