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arXiv · 1303.4406

Extensions of translation invariant valuations on polytopes

Wolfram Hinderer·Daniel Hug·Wolfgang Weil
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Abstract

We study translation invariant, real-valued valuations on the class of convex polytopes in Euclidean space and discuss which continuity properties are sufficient for an extension of such valuations to all convex bodies. For this purpose, we introduce flag support measures of convex bodies via a local Steiner formula and derive some of the properties of these measures.

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Wolfram Hinderer, Daniel Hug, Wolfgang Weil. 2014-04-03. Extensions of translation invariant valuations on polytopes. https://doi.org/10.1112/s0025579314000187

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