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Keywords:
measurable multifunction; set-valued conditional expectation; Levy's theorem; support function; Kuratowski-Mosco convergence of sets
measurable multifunction; set-valued conditional expectation; Levy's theorem; support function; Kuratowski-Mosco convergence of sets
Summary:
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.
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