Abstract
The goal of the present chapter is to translate displacement convexity inequalities of the form “the graph of a convex function lies below the chord” into inequalities of the form “the graph of a convex function lies above the tangent” — just as in statements (ii) and (iii) of Proposition 16.2. This corresponds to the limit t → 0 in the convexity inequality.
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© 2009 Springer-Verlag Berlin Heidelberg
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Villani, C. (2009). Infinitesimal displacement convexity. In: Optimal Transport. Grundlehren der mathematischen Wissenschaften, vol 338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71050-9_20
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DOI: https://doi.org/10.1007/978-3-540-71050-9_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71049-3
Online ISBN: 978-3-540-71050-9
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