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arXiv · 1703.06867

Translation invariant valuations on quasi-concave functions

Andrea Colesanti·Nico Lombardi·Lukas Parapatits
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Abstract

We study real-valued, continuous and translation invariant valuations defined on the space of quasi-concave functions of N variables. In particular, we prove a homogeneous decomposition theorem of McMullen type, and we find a representation formula for those valuations which are N-homogeneous. Moreover, we introduce the notion of Klain's functions for these type of valuations.

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Andrea Colesanti, Nico Lombardi, Lukas Parapatits. 2017-03-20. Translation invariant valuations on quasi-concave functions. https://arxiv.org/abs/1703.06867

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