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Integration of positive constructible functions against Euler characteristic and dimension

R. Cluckers·M. Edmundo
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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.

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R. Cluckers, M. Edmundo. 2006-07-06. Integration of positive constructible functions against Euler characteristic and dimension. https://arxiv.org/abs/math/0607165

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