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Conditional expectation of Pettis integrable unbounded random sets. (English) Zbl 1455.60010

Summary: In this paper we established new results of existence of conditional expectation for closed convex and unbounded Pettis integrable random sets without assuming the Radon Nikodym property of the Banach space. As application, new versions of multivalued Lévy’s martingale convergence theorem are proved by using the Slice and the linear topologies.

MSC:

60B11 Probability theory on linear topological spaces
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
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