OPTIMAL TRANSPORT AND THE GEOMETRY OF LpRq
نویسندگان
چکیده
A classical theorem due to R. Phelps states that if C is a weakly compact set in a Banach space E, the strongly exposing functionals form a dense subset of the dual space E. In this paper, we look at the concrete situation where C L1pRdq is the closed convex hull of the set of random variables Y P L1pRdq having a given law ν. Using the theory of optimal transport, we show that every random variableX P L8pRdq, the law of which is absolutely continuous with respect to the Lebesgue measure, strongly exposes the set C. Of course these random variables are dense in L8pRdq.
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