Constructible motivic functions and motivic integration
  We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative framework, in which we develop a relative version of motivic integration. These results have been announced in math.AG/0403349 and math.AG/0403350.   Main results and statements unchanged. Many minor slips corrected and some details added. 
R. Cluckers, F. Loeser