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Conditional expectation of Pettis integrable unbounded random sets
Mohamed El Harami 대한수학회 2020 대한수학회지 Vol.57 No.2
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.
CONDITIONAL EXPECTATION OF PETTIS INTEGRABLE UNBOUNDED RANDOM SETS
El Harami, Mohamed Korean Mathematical Society 2020 대한수학회지 Vol.57 No.2
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.
PETTIS CONDITIONAL EXPECTATION OF CLOSED CONVEX RANDOM SETS IN A BANACH SPACE WITHOUT RNP
Akhiat, Fattah,El Harami, Mohamed,Ezzaki, Fatima Korean Mathematical Society 2018 대한수학회지 Vol.55 No.4
In this paper we study the existence of conditional expectation for closed and convex valued Pettis-integrable random sets without assuming the Radon Nikodym property of the Banach space. New version of multivalued dominated convergence theorem of conditional expectation and multivalued $L{\acute{e}}vy^{\prime}s$ martingale convergence theorem for integrable and Pettis integrable random sets are proved.
Pettis conditional expectation of closed convex random sets in a Banach space without $RNP$
Fattah Akhiat,Mohamed El Harami,Fatima Ezzaki 대한수학회 2018 대한수학회지 Vol.55 No.4
In this paper we study the existence of conditional expectation for closed and convex valued Pettis-integrable random sets without assuming the Radon Nikodym property of the Banach space. New version of multivalued dominated convergence theorem of conditional expectation and multivalued L\'evy's martingale convergence theorem for integrable and Pettis integrable random sets are proved.