On the conditional expectation and convergence properties of random sets

Papageorgiou, Nikolaos S.

doi:10.1090/S0002-9947-1995-1290728-9

On the conditional expectation and convergence properties of random sets
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Trans. Amer. Math. Soc. 347 (1995), 2495-2515 Request permission

Abstract:

In this paper we study random sets, with values in a separable Banach space. First we establish several useful properties of the set-valued conditional expectation and then prove some convergence theorems for set-valued amarts and uniform amarts, using the weak, Kuratowski-Mosco and Hausdorff modes of set convergence.

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