Hadwiger's Theorem for definable functions

被引：20

作者：

Baryshnikov, Y. ^{[1
,2
]}

Ghrist, R. ^{[3
,4
]}

Wright, M. ^{[5
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL USA

[2] Univ Illinois, Dept Elect & Comp Engn, Urbana, IL USA

[3] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

[4] Univ Penn, Dept Elect Syst Engn, Philadelphia, PA 19104 USA

[5] Huntington Univ, Dept Math, Huntington, IN USA

来源：

ADVANCES IN MATHEMATICS | 2013年 / 245卷

关键词：

Valuations; Hadwiger measure; Intrinsic volumes; Euler characteristic; VALUATIONS; CURVATURE;

D O I：

10.1016/j.aim.2013.07.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Hadwiger's Theorem states that E-n-invariant convex-continuous valuations of definable sets in R-n are linear combinations of intrinsic volumes. We lift this result from sets to data distributions over sets, specifically, to definable R-valued functions on R-n. This generalizes intrinsic volumes to (dual pairs of) non-linear valuations on functions and provides a dual pair of Hadwiger classification theorems. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：573 / 586

页数：14

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