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

Tobias Kaiser. "On convergence of integrals in o-minimal structures on archimedean real closed fields." Annales Polonici Mathematici 87.1 (2005): 175-192. <http://eudml.org/doc/280486>.

@article{TobiasKaiser2005,
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.},
author = {Tobias Kaiser},
journal = {Annales Polonici Mathematici},
keywords = {o-minimal structures; integration; Hardy fields},
language = {eng},
number = {1},
pages = {175-192},
title = {On convergence of integrals in o-minimal structures on archimedean real closed fields},
url = {http://eudml.org/doc/280486},
volume = {87},
year = {2005},
}

TY - JOUR
AU - Tobias Kaiser
TI - On convergence of integrals in o-minimal structures on archimedean real closed fields
JO - Annales Polonici Mathematici
PY - 2005
VL - 87
IS - 1
SP - 175
EP - 192
AB - 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.
LA - eng
KW - o-minimal structures; integration; Hardy fields
UR - http://eudml.org/doc/280486
ER -