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).