Translation invariant valuations on quasi-concave functions
Metric Geometry
2017-03-21 v1
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.
Keywords
Cite
@article{arxiv.1703.06867,
title = {Translation invariant valuations on quasi-concave functions},
author = {Andrea Colesanti and Nico Lombardi and Lukas Parapatits},
journal= {arXiv preprint arXiv:1703.06867},
year = {2017}
}