Integration II

Integration is the sixth and last of the books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology and  Topological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author's Théories Spectrales, an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.

The first volume of the English translation comprises Chapters 1-6; the present volume completes the translation with the remaining Chapters 7-9.

Chapters 1-5 received very substantial revisions in a second edition, including changes to some fundamental definitions. Chapters 6-8 are based on the first editions of Chapters 1-5. The English edition has given the author the opportunity to correct misprints, update references, clarify the concordance of Chapter 6 with the second editions of Chapters 1-5, and revise the definition of a key concept in Chapter 6 (measurable equivalence relations).

From the reviews:

"This volume of the new English edition of the famous series of monographs contains chapters … which are devoted to integration theory. … It contains the basic theory on locally compact groups, an abstract theory, applications and examples. … Due to an abstract, general and exact exposition, the textbook may also be of interest for specialists in the topic." (EMS Newsletter, June, 2006)