Hausdorff measure on o-minimal structures

Details Hausdorff measure on o-minimal structures Hausdorff measure on o-minimal structures

2010-11-07

arxiv.org/abs/1011.1629v1

Mathematics

Logic

22 pages

Scientific paper

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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