Hadwiger's Theorem for Definable Functions
Differential Geometry
2013-07-02 v3 Geometric Topology
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.
Cite
@article{arxiv.1203.6120,
title = {Hadwiger's Theorem for Definable Functions},
author = {Yuliy Baryshnikov and Robert Ghrist and Matthew Wright},
journal= {arXiv preprint arXiv:1203.6120},
year = {2013}
}
Comments
14 pages, 3 figures