Conditional expectation of Pettis integrable unbounded random sets
J. Korean Math. Soc. 2020 Vol. 57, No. 2, 359-381
Published online March 1, 2020
Mohamed El Harami
Higher School of Technology
Abstract : 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 L\'evy's martingale convergence theorem are proved by using the Slice and the linear topologies.
Keywords : Pettis integral, closed convex random sets, Pettis conditional expectation, Levy's theorem, Slice and linear topologies
MSC numbers : Primary 60H05, 60H25; Secondary 28B20
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