• Title/Summary/Keyword: closed convex random sets

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PETTIS CONDITIONAL EXPECTATION OF CLOSED CONVEX RANDOM SETS IN A BANACH SPACE WITHOUT RNP

  • Akhiat, Fattah;El Harami, Mohamed;Ezzaki, Fatima
    • Journal of the Korean Mathematical Society
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    • v.55 no.4
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    • pp.833-848
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    • 2018
  • 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.

CONDITIONAL EXPECTATION OF PETTIS INTEGRABLE UNBOUNDED RANDOM SETS

  • El Harami, Mohamed
    • Journal of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.359-381
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    • 2020
  • 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.