  We study Lebesgue integration of sums of products of globally subanalytic
functions and their logarithms, called constructible functions. Our first
theorem states that the class of constructible functions is stable under
integration. The second theorem treats integrability conditions in Fubini-type
settings, and the third result gives decay rates at infinity for constructible
functions. Further, we give preparation results for constructible functions
related to integrability conditions.
