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Preprint Number 690
690. Jana Marikova, Masahiro Shiota
Measuring definable sets in o-minimal fields
Submission date: 19 February 2014.
We introduce a non real-valued measure on the definable sets contained in the finite part of a cartesian power of an o-minimal field R. The measure takes values in an ordered semiring, the Dedekind completion of a quotient of R. We show that every measurable subset of R^n with non-empty interior has positive measure, and that the measure is preserved by definable C^1-diffeomorphisms with Jacobian determinant equal to ±1.
Mathematics Subject Classification: 03C64
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