Elements of mathematics. Integration I: Chapters 1–6. Translated from the 1959, 1965 and 1967 French originals by Sterling K. Berberian. (English) Zbl 1095.28001

Berlin: Springer (ISBN 3-540-41129-1/hbk). xv, 472 p. (2004).
Publisher’s description: “Intégration” is the sixth and last of the books that form the core of the Bourbaki series; it draws abundantly on the preceding five books, expecially 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” (1967; Zbl 0152.32603), an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.
The present volume comprises Chapters 1–6 in English translation (a second volume contains the remaining Chapters 7–9 (2001; Zbl 1095.28002). 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 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).


28-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
28A12 Contents, measures, outer measures, capacities
28B05 Vector-valued set functions, measures and integrals
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
46G10 Vector-valued measures and integration
46G12 Measures and integration on abstract linear spaces