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Monotone maps preserving periodic measures

Abstract : Following the method of McCann [8], we shaw that given two (regular enough) periodic measures mu and nu on R-d, there exists a monotone function (ie: the gradient of a convex function) which pushes-forward mu onto nu. (C) Academie des Sciences/Elsevier, Paris.
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Dario Cordero-Erausquin. Monotone maps preserving periodic measures. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 1999, 329 (3), pp.199--202. ⟨10.1016/S0764-4442(00)88593-6⟩. ⟨hal-00693880⟩

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