Journal of the
Korean Mathematical Society JKMS

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.

Keywords: closed convex random sets, Aumann Pettis integral, Pettis integral, conditional expectation, L\'evy theorem, dominated convergence theorem.

MSC numbers: Primary 58J65, 60H05, 60H25