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Hausdorff measure on o-minimal structures
Published 7 Nov 2010 in math.LO | (1011.1629v1)
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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