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 | |
出版ステータス | 出版済み - 10月 1 2013 |
外部発表 | はい |
All Science Journal Classification (ASJC) codes
- 数学 (全般)