The Cauchy-Crofton formula and the Whitney arc property for definable sets
Logic
2010-11-09 v2
Abstract
We use the Cauchy-Crofton formula to show that every definable cell (bounded by a ball with rational radius) in an O-minimal expansion of a field extension of the real numbers satisfies the Whitney arc property.
Keywords
Cite
@article{arxiv.0812.2735,
title = {The Cauchy-Crofton formula and the Whitney arc property for definable sets},
author = {Elisa Vasquez Rifo},
journal= {arXiv preprint arXiv:0812.2735},
year = {2010}
}
Comments
8 pages, This paper has been withdrawn by the author. The third sentence of the proof of Theorem 5.6 contained an error; the results are subsumed and extended by the paper "Hausdorff measure on o-minimal structures" with A. Fornasiero