This text contains a basic introduction to abstract measure theory and the Lebesgue integral. Most of the standard topics in measure and integration theory are discussed. In addition, topics on the Hewitt-Yosida decomposition, the Nikodym and Vitali-Hahn-Saks theorems and material on finitely additive set functions are explored. There is an introductory section on functional analysis, including the three basic principles, which is used to discuss many of the classic Banach spaces of functions and their duals. There is also a chapter on Hilbert space and the Fourier transform.

- Contains a thorough treatment of each of the integrals of Riemann, Lebesgue, Henstock-Kurzweil and McShane
- Discusses the weaknesses of the various integrals and presents a comparison of the integrals
- Abundant supply of exercises and examples
- Chapters can be used independently

The book uses classical problems to motivate a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil and McShane, showing how new theories of integration were developed to solve problems that earlier integration theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and could be used separately in teaching a portion of an introductory real analysis course. There is a sufficient supply of exercises to make this...