dc.contributor.author Ekeland, Ivar dc.contributor.author Schachermayer, Walter dc.date.accessioned 2015-04-07T11:37:24Z dc.date.available 2015-04-07T11:37:24Z dc.date.issued 2014 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/14889 dc.language.iso en en dc.subject Transport en dc.subject.ddc 519 en dc.title Optimal transport and the geometry of L1(Rd) en dc.type Article accepté pour publication ou publié dc.description.abstracten 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 $E^{\prime }$. In this paper, we look at the concrete situation where $C\subset L^{1}(\mathbb{R}^{d})$ is the closed convex hull of the set of random variables $Y\in L^{1}(\mathbb{R}^{d})$ having a given law $\nu$. Using the theory of optimal transport, we show that every random variable $X\in L^{\infty }(\mathbb{R}^{d})$, 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 $L^{\infty }(\mathbb{R}^{d})$ en dc.relation.isversionofjnlname Proceedings of the American Mathematical Society dc.relation.isversionofjnlvol 142 en dc.relation.isversionofjnldate 2014 dc.relation.isversionofjnlpages 3585-3596 en dc.relation.isversionofdoi http://dx.doi.org/10.1090/S0002-9939-2014-12094-6 en dc.relation.isversionofjnlpublisher AMS en dc.subject.ddclabel Probabilités et mathématiques appliquées en dc.relation.forthcoming non en dc.relation.forthcomingprint non en
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