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arXiv · 1709.08959

Continuity and representation of valuations on star bodies

Pedro Tradacete·Ignacio Villanueva
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Abstract

It is shown that every continuous valuation defined on the $n$-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 $n$-dimensional star bodies that arise as the restriction of a measure on $\mathbb R^n$.

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Pedro Tradacete, Ignacio Villanueva. 2017-09-26. Continuity and representation of valuations on star bodies. https://arxiv.org/abs/1709.08959

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