Geodesic
Monotone Valuations on the Space of Convex Functions
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞. We study the valuations defined on Cn which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. We prove integral representations formulas for such valuations which are, in addition, simple or homogeneous.
Mots-clés : convex functions, valuations, convex bodies, sub-level sets, intrinsic volumes 
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Cavallina, L.; Colesanti, A. Monotone Valuations on the Space of Convex Functions. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a11/