On the continuity of the vector valued and set valued conditional expectations

Nikolaos S. Papageorgiou

International Journal of Mathematics and Mathematical Sciences, 1989, vol. 12, 1-10

Abstract:

In this paper we study the dependence of the vector valued conditional expectation (for both single valued and set valued random variables), on the σ–field and random variable that determine it. So we prove that it is continuous for the L 1 ( X ) convergence of the sub–σ–fields and of the random variables. We also present a sufficient condition for the L 1 ( X ) –convergence of the sub–σ–fields. Then we extend the work to the set valued conditional expectation using the Kuratowski–Mosco (K–M) convergence and the convergence in the Δ–metric. We also prove a property of the set valued conditional expectation.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:138321

DOI: 10.1155/S016117128900061X

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