On convergence of integrals in $o$-minimal structures on archimedean real closed fields
Volume 87 / 2005
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.
