Title: A convergence theorem for convex set valued supermartingales<sup>∗</sup>
Abstract: Functions whose values are convex subsets provide a natural setting for the study of goal uncertainty in decision making. In fact under reasonable assumptions the successive estimates of the convex valued conditional expectations of the utility function form a supermartingale. It is of course important to determine if such estimates converge It is shown that if {Fn, Hn} is a supermartingale where Fn has as values convex subsets of a Banach space X with separable dual and provided that Fn is “uniformly integrable” then Fn converges in some appropriate mode made precise in the work
Publication Year: 1985
Publication Date: 1985-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 28
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