Integration of positive constructible functions against Euler characteristic and dimension
Logic
2014-04-29 v1
Abstract
Following recent work of R. Cluckers and F. Loeser [Fonctions constructible et integration motivic I, C. R. Math. Acad. Sci. Paris 339 (2004) 411 - 416] on motivic integration, we develop a direct image formalism for positive constructible functions in the globally subanalytic context. This formalism is generalized to arbitrary first-order logic models and is illustrated by several examples on the p-adics, on the Presburger structure and on o-minimal expansions of groups. Furthermore, within this formalism, we define the Radon transform and prove the corresponding inversion formula.
Cite
@article{arxiv.math/0607165,
title = {Integration of positive constructible functions against Euler characteristic and dimension},
author = {R. Cluckers and M. Edmundo},
journal= {arXiv preprint arXiv:math/0607165},
year = {2014}
}
Comments
To appear in Journal of Pure and Applied Algebra; 8 pages