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On convergence of integrals in o-minimal structures on archimedean real closed fields

Tobias Kaiser (2005)

Annales Polonici Mathematici

We define a notion of volume for sets definable in an o-minimal structure on an archimedean real closed field. We show that given a parametric family of continuous functions on the positive cone of an archimedean real closed field definable in an o-minimal structure, the set of parameters where the integral of the function converges is definable in the same structure.

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