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Hausdorff measure on o-minimal structures
A. Fornasiero, E. Vasquez Rifo
Journal:

The Journal of Symbolic Logic / Volume 77 / Issue 2 / June 2012

Published online by Cambridge University Press:

12 March 2014, pp. 631-648

Print publication:

June 2012
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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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Hausdorff measure on o-minimal structures