Hausdorff measure on o-minimal structures

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.

22 pages

Cited by in corpus (2)

• Lebesgue measure theory and integration theory on non-archimedean real closed fields with archimedean value group
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