This is a conventional development of integration theory, starting with measure spaces. The Author’s Note (p. vii) states that “The goal here is concision, clarity, and accuracy,” and the book meets these goals. By American standards this is not a “Course”, as it has no exercises or motivation, and only a modest set of examples. The present volume is a reprint of the original 1996 publication.
I think this book works best as a review or as an introduction to the more abstract theories of integration. It is too abstract for a first course in integration, as it starts immediately with the most abstract theories and only (a great deal later) deals with integration on the real line. A book that takes a similar approach, but with more exercises and more concreteness, is Hewitt & Stromberg’s Real and Abstract Analysis.
Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.org, a math help site that fosters inquiry learning.