Abstract
We consider Hilbert and Funk geometries on a strongly convex domain in Euclidean space. We show that, with respect to the Lebesgue measure on the domain, the Hilbert and Funk metrics have bounded and constant negative weighted Ricci curvature, respectively. As a corollary, these metric measure spaces satisfy the curvature-dimension condition in the sense of Lott, Sturm and Villani.
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