Hausdorff measure on o-minimal structures

Journal of Symbolic Logic 77 (2):631-648 (2012)

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 O-minimality   Hausdorff measure   Whitney arc property   Cauchy-Crofton   coarea
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DOI 10.2178/jsl/1333566642
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