Submission date: 19 February 2014.

Abstract:

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

Keywords and phrases:

Full text arXiv 1402.4787: pdf, ps.