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.
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页码：573 / 586
页数：14
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