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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the conditional expectation and convergence properties of random sets


Author: Nikolaos S. Papageorgiou
Journal: Trans. Amer. Math. Soc. 347 (1995), 2495-2515
MSC: Primary 60G48; Secondary 28B20, 60D05
MathSciNet review: 1290728
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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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DOI: https://doi.org/10.1090/S0002-9947-1995-1290728-9
Keywords: Set-valued conditional expectation, set-valued amarts and uniform amarts, weak convergence, Kuratowski-Mosco convergence, Hausdorff metric, optional sampling
Article copyright: © Copyright 1995 American Mathematical Society