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Integration II: Chapters 79 (Elements of Mathematics),New
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Integrationis 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 Thories 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 16; the present volume completes the translation with the remaining Chapters 79.Chapters 15 received very substantial revisions in a second edition, including changes to some fundamental definitions. Chapters 68 are based on the first editions of Chapters 15. 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 15, and revise the definition of a key concept in Chapter 6 (measurable equivalence relations).
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