From Preface:
This undergraduate textbook on the theory of Lebesgue integration is designed for use in a one-semester or two-quarter undergraduate course in the junior or senIor year.
By "integration theory" we mean that the technique of integrating functions is developed first and is then used for the measuring of sets, rather than the other way around. The choice of the "integration first" approach was mostly a matter of taste, but also made it possible to arrive at meaningful and interesting theorems on integration as early as possible in the course.