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arXiv · 1011.1629

Hausdorff measure on o-minimal structures

Antongiulio Fornasiero·Elisa Vasquez Rifo
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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.

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Antongiulio Fornasiero, Elisa Vasquez Rifo. 2010-11-07. Hausdorff measure on o-minimal structures. https://doi.org/10.2178/jsl%2F1333566642

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