STABILITY UNDER INTEGRATION OF SUMS OF PRODUCTS OF REAL GLOBALLY SUBANALYTIC FUNCTIONS AND THEIR LOGARITHMS

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.