Abstract
Following recent work of R. Cluckers and F. Loeser [Fonctions constructible et intégration 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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