We consider the space of real-valued convex functions defined in the n-dimensional Euclidean space. We study the valuations defined on the space of these functions, 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.
Monotone valuations on the space of convex functions / Cavallina, Lorenzo; Colesanti, Andrea. - STAMPA. - 3:(2015), pp. 167-211. [10.1515/agms-2015-0012]
Monotone valuations on the space of convex functions
CAVALLINA, LORENZO;COLESANTI, ANDREA
2015
Abstract
We consider the space of real-valued convex functions defined in the n-dimensional Euclidean space. We study the valuations defined on the space of these functions, 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.
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