Hadwiger's Theorem for definable functions

Y. Baryshnikov, R. Ghrist, M. Wright

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

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

Original languageEnglish
Pages (from-to)573-586
Number of pages14
JournalAdvances in Mathematics
Volume245
DOIs
Publication statusPublished - Oct 1 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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