Edmundo, MárioCluckers, R.2014-01-222014-01-222007-02Edmundo, Mário; Cluckers, R. - Integration of positive constructible functions against Euler characteristic and dimension. "Journal of Pure and Applied Algebra" [Em linha]. ISSN 0022-4049. Vol. 208, nº 2 (2007), p. 1-100022-4049http://hdl.handle.net/10400.2/2856Following 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.engO-minimal structuresEuler integrationjournal article