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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-14,
author = {Tobias Kaiser},
title = {On convergence of integrals in o-minimal structures on archimedean real closed fields},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {175-192},
zbl = {1097.03030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-14}
}
Tobias Kaiser. On convergence of integrals in o-minimal structures on archimedean real closed fields. Annales Polonici Mathematici, Tome 85 (2005) pp. 175-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-14/