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General Pettis Conditional expectation and convergence theorems

M. El Harami, F. Ezzaki


In this paper we present a new existence results of conditional expectation for Pettis integrable
random variables (resp, random sets) defined in a general measure space (i.e the measure is not necessarily finite) with values in a separable Banach space (resp, with convex and weakly compact values). As applications we shall extend the classical Levy’s theorem in a more general context where Pettis integrable random variables (resp, random sets) are considered. Also we give a new version of dominated convergence theorem of
Pettis conditional expectation.


Pettis integral, conditional expectation, Levy’s theorem, dominated convergence theorem, random sets, Mosco-convergence.

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