Hausdorff measure on o-minimal structures
Logic
2021-11-23 v1
Abstract
We introduce the Hausdorff measure for definable sets in an o-minimal structure, and prove the Cauchy-Crofton and co-area formulae for the o-minimal Hausdorff measure. We also prove that every definable set can be partitioned into "basic rectifiable sets", and that the Whitney arc property holds for basic rectifiable sets.
Cite
@article{arxiv.1011.1629,
title = {Hausdorff measure on o-minimal structures},
author = {Antongiulio Fornasiero and Elisa Vasquez Rifo},
journal= {arXiv preprint arXiv:1011.1629},
year = {2021}
}
Comments
22 pages