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.Comment: To appear in Journal of Pure and Applied Algebra; 8 page