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arXiv · 1203.6120

Hadwiger's Theorem for Definable Functions

Yuliy Baryshnikov·Robert Ghrist·Matthew Wright
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Abstract

Hadwiger's Theorem states that Euclidean-invariant convex-continuous valuations of definable sets are linear combinations of intrinsic volumes. We lift this result from sets to data distributions over sets, specifically, to definable real-valued functions on n-dimensional Euclidean space. This generalizes intrinsic volumes to (dual pairs) of non-linear valuations on functions and provides a dual pair of Hadwiger classification theorems.

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Yuliy Baryshnikov, Robert Ghrist, Matthew Wright. 2013-06-28. Hadwiger's Theorem for Definable Functions. https://arxiv.org/abs/1203.6120

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