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Hausdorff measure on o-minimal structures

  • A. Fornasiero (a1) and E. Vasquez Rifo (a2)


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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