Real Algebraic and Analytic Geometry |

An additive measure in o-minimal expansions of fields.

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Submission: 2003, October 31.

*Abstract:
Given an o-minimal structure M which expands a field, we define,
for each positive integer d, a real valued additive measure on a
Boolean algebra of subsets of M^d and we prove that all the
definable sets included in the finite part Fin(M^d) of M^d are
measurable. When the domain of M is IR we obtain the Lebesgue
measure, but restricted to a proper subalgebra of that of the
Lebesgue measurable sets. Our measure has good logical
properties, being invariant under elementary extensions and under
expansions of the language.*

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