Real Algebraic and Analytic Geometry

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66. Alessandro Berarducci, Margarita Otero:
An additive measure in o-minimal expansions of fields.

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Submission: 2003, October 31.

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.

Full text, 11p.: dvi 50k, ps.gz 151k, pdf 191k.

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