Journal of Pure and Applied Algebra vol:208 issue:2 pages:691-698
Following recent work of R. Cluckers; and F. Loeser [Fonctions constructible et integration motivic 1, 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. (c) 2006 Elsevier B.V. All rights reserved.