Loci of Integrability, Zero Loci, and Stability Under Integration for Constructible Functions on Euclidean Space with Lebesgue Measure

We introduce and study loci of integrability. We prove a correspondence between zero loci and loci of integrability for constructible functions on Euclidean space, where a function is called constructible if it is a sum of products of globally subanalytic functions and of logarithms of globally subanalytic functions. We generalize the main result of the authors in Cluckers and Miller [Stability un...