Monotone Valuations on the Space of Convex Functions

L. Cavallina, A. Colesanti
2015 Analysis and Geometry in Metric Spaces  
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.
doi:10.1515/agms-2015-0012 fatcat:kitn722uu5arbig72hmlaubuhm