English

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.

Keywords

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

R2 v1 2026-06-21T16:40:08.259Z