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Pettis conditional expectation of closed convex random sets in a Banach space without $RNP$

Fattah Akhiat|Mohamed El Harami|Fatima Ezzaki
대한수학회 (The Korean Mathematical Society)|2018.07|대한수학회지 (Journal of the KMS)|제55권 제4호|pp. 833-848

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참고문헌

키워드

conditional expectationclosed convex random setsAumann Pettis integralPettis integralL\'evy theoremdominated convergence theorem.
주제분류수학

초록

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.

Abstract

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.

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