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.
Translation invariant valuations on quasi-concave functions / Colesanti, Andrea; Lombardi, Nico; Lukas, Parapatits. - In: STUDIA MATHEMATICA. - ISSN 0039-3223. - STAMPA. - 243:(2018), pp. 79-99. [10.4064/sm170323-7-7]
Translation invariant valuations on quasi-concave functions
Andrea Colesanti;Nico Lombardi;
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 these type of valuations.
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