Translation invariant valuations on quasi-concave functions
Volume 243 / 2018
Studia Mathematica 243 (2018), 79-99
MSC: Primary 26B25; Secondary 52B45, 52A41.
DOI: 10.4064/sm170323-7-7
Published online: 29 January 2018
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 this type of valuations.
