Submission date: 17 November 2010.

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.

Mathematics Subject Classification: Primary: 03C64; Secondary: 28A75

Keywords and phrases: Hausdorff measure, o-minimality, Cauchy-Crofton formula, Whitney arc property.

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