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

Volume 87 / 2005

Tobias Kaiser Annales Polonici Mathematici 87 (2005), 175-192 MSC: 03C64, 12J15, 28B15. DOI: 10.4064/ap87-0-14

Abstract

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.

Authors

  • Tobias KaiserDepartment of Mathematics
    University of Regensburg
    Universitätsstr. 31
    D-93040 Regensburg, Germany
    e-mail

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