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Hausdorff measure on o-minimal structures

Published online by Cambridge University Press:  12 March 2014

A. Fornasiero  and
E. Vasquez Rifo
A. Fornasiero
Affiliation:
Institut für Mathematische Logik, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62. 48149 Münster, Germany, E-mail: antongiulio.fornasiero@googlemail.com
E. Vasquez Rifo
Affiliation:
Instituto de Matemática y Física, Universidad de Talca, Talca, Chile, E-mail: evasquez@inst-mat.utalca.cl
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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.

Keywords

O-minimalityHausdorff measureWhitney arc propertyCauchy-Crofton coarea
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 2 , June 2012 , pp. 631 - 648
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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