Continuity and representation of valuations on star bodies
Metric Geometry
2017-09-27 v1 Functional Analysis
Abstract
It is shown that every continuous valuation defined on the -dimensional star bodies has an integral representation in terms of the radial function. Our argument is based on the non-trivial fact that continuous valuations are uniformly continuous on bounded sets. We also characterize the continuous valuations on the -dimensional star bodies that arise as the restriction of a measure on .
Cite
@article{arxiv.1709.08959,
title = {Continuity and representation of valuations on star bodies},
author = {Pedro Tradacete and Ignacio Villanueva},
journal= {arXiv preprint arXiv:1709.08959},
year = {2017}
}