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dc.contributor.authorEkeland, Ivar
dc.contributor.authorSchachermayer, Walter
dc.date.accessioned2015-04-07T11:37:24Z
dc.date.available2015-04-07T11:37:24Z
dc.date.issued2014
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14889
dc.language.isoenen
dc.subjectTransporten
dc.subject.ddc519en
dc.titleOptimal transport and the geometry of L1(Rd)en
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenA 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.isversionofjnlnameProceedings of the American Mathematical Society
dc.relation.isversionofjnlvol142en
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages3585-3596en
dc.relation.isversionofdoihttp://dx.doi.org/10.1090/S0002-9939-2014-12094-6en
dc.relation.isversionofjnlpublisherAMSen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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