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Monotone valuations on the space of convex functions

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arxiv 1502.06729 v1 pith:FHJHWNHA submitted 2015-02-24 math.MG

L. Cavallina , A. Colesanti This is my paper · ORCID
classification math.MG
keywords spacefunctionsvaluationsconvexdefinedinfinitymonotoneadditionally
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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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