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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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[B004] Berarducci, A. and Otero, M.. An additive measure in o-minimal expansions of fields. The Quarterly Journal of Mathematics, vol. 55 (2004). no. 4. pp. 411419.
[BP98] Baisalov, Y. and Poizat, B., Paires de structures o-minirnales. this Journal, vol. 63 (1998). no. 2, pp. 570578.
[Dries98] van Den Dries, L., Tame topology and o-minimal structures. London Mathematical Society Lecture Note Series, vol. 248, Cambridge University Press. Cambridge. 1998.
[Dries03] van Den Dries, L., Limit sets in o-minimal structures. O-minimal Structures, Proceedings of the RAAG Summer School Lisbon 2003 (Edmundo, M., Richardson, D., and Wilkie, A., editors). Lecture Notes in Real Algebraic and Analytic Geometry, Cuvillier Verlag. 2005.
[Halmos50] Halmos, P. R., Measure Theory, D. Van Nostrand Company, Inc., New York, 1950.
[K92] Kurdyka, K., On a subanalytic stratification satisfying a Whitney property with exponent 1. Real algebraic geometry proceedings (Rennes, 1991). Lecture Notes in Mathematics, vol. 1524, Springer, Berlin, 1992. pp. 316322.
[M09] Maříková, J., The structure on the real field generated by the standard part map on an o-minimal expansion of a real closed field, Israel Journal of Mathematics, vol. 171 (2009), pp. 175195.
[MillerO1] Miller, C., Expansions of dense linear orders with the intermediate value property, this Journal, vol. 66 (2001). no. 4. pp. 17831790.
[Morgan88] Morgan, F., Geometric measure theory, Academic Press Inc., 1988. An introduction to Federer's book by the same title.
[P08] Pawłucki, W., Lipschitz cell decomposition in o-minimal structures. I, Illinois Journal of Mathematics, vol. 52 (2008). no. 3, pp. 10451063.
[PW06] Pila, J. and Wilkie, A. J., The rational points of a definable set, Duke Mathematical Journal. vol. 133 (2006), no. 3, pp. 591616.
[VR06] Rifo, E. Vasquez, Geometric partitions of definable sets, Ph.D. thesis, The University of Wisconsin-Madison, 08 2006.
[W00] Warner, F., Foundations of differentiable manifolds and lie groups. Springer-Verlag, 2000.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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