Hadwiger's Theorem for definable functions

Y. Baryshnikov; R. Ghrist; M. Wright

doi:10.1016/j.aim.2013.07.001

Hadwiger's Theorem for definable functions

Y. Baryshnikov, R. Ghrist, M. Wright

研究成果: Contribution to journal › Article › 査読

19 被引用数 (Scopus)

抄録

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.

本文言語	英語
ページ（範囲）	573-586
ページ数	14
ジャーナル	Advances in Mathematics
巻	245
DOI	https://doi.org/10.1016/j.aim.2013.07.001
出版ステータス	出版済み - 10 1 2013
外部発表	はい

All Science Journal Classification (ASJC) codes

Mathematics(all)

文献へのアクセス

10.1016/j.aim.2013.07.001

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引用スタイル

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