Geodesic
Monotone Valuations on the Space of Convex Functions
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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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 
@article{AGMS_2015_3_1_a11,
     author = {Cavallina, L. and Colesanti, A.},
     title = {Monotone {Valuations} on the {Space} of {Convex} {Functions}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2015},
     volume = {3},
     number = {1},
     zbl = {1321.26027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a11/}
}
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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/