Changes of Variable

Abstract

We have now developed the basic theory of Lebesgue integration. However, thus far we have nearly no tools with which to compute the integrals which we have shown to exist. The purpose of the present chapter is to introduce a technique which often makes evaluation, or at least estimation, possible. The technique is that of changing variables. In this introduction, we describe the technique in complete generality. In ensuing sections we will give some examples of its applications.