Iterated Integrals and the Fubini Theorem

In the previous chapter we introduced the notion of the integral for a function of n variables. We now take up the problem of computing this integral. The basic result is the Fubini theorem, which effectively reduces the problem of integrating a function of n variables to the evaluation of n ordinary integrals of a function of one variable. We give two forms of the Fubini theorem and show how to apply it to some problems.