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arXiv · 1502.06729

Monotone valuations on the space of convex functions

L. Cavallina·A. Colesanti
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Abstract

We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. Among these valuations we prove integral representation formulas for those which are, additionally, simple or homogeneous.

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L. Cavallina, A. Colesanti. 2015-02-24. Monotone valuations on the space of convex functions. https://doi.org/10.1515/agms-2015-0012

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