Characterizing the dual mixed volume via additive functionals
Functional Analysis
2013-12-17 v1 Metric Geometry
Abstract
Integral representations are obtained of positive additive functionals on finite products of the space of continuous functions (or of bounded Borel functions) on a compact Hausdorff space. These are shown to yield characterizations of the dual mixed volume, the fundamental concept in the dual Brunn-Minkowski theory. The characterizations are shown to be best possible in the sense that none of the assumptions can be omitted. The results obtained are in the spirit of a similar characterization of the mixed volume in the classical Brunn-Minkowski theory, obtained recently by Milman and Schneider, but the methods employed are completely different.
Cite
@article{arxiv.1312.4072,
title = {Characterizing the dual mixed volume via additive functionals},
author = {Paolo Dulio and Richard J. Gardner and Carla Peri},
journal= {arXiv preprint arXiv:1312.4072},
year = {2013}
}