Measuring definable sets in o-minimal fields

Jana Maříková; Masahiro Shiota

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arXiv · 1402.4787

Measuring definable sets in o-minimal fields

Jana Maříková·Masahiro Shiota

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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 $\pm 1$.

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BibTeX RIS

Jana Maříková, Masahiro Shiota. 2014-02-19. Measuring definable sets in o-minimal fields. https://arxiv.org/abs/1402.4787

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