Integration of positive constructible functions against Euler characteristic and dimension

Details Integration of positive constructible functions against Euler characteristic and dimension Integration of positive constructible functions against Euler characteristic and dimension

2006-07-06

arxiv.org/abs/math/0607165v1

Mathematics

Logic

To appear in Journal of Pure and Applied Algebra; 8 pages

Scientific paper

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.

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