Integration 1: Chapters 1-6.: Vol 1 (Elements of Mathematics) Book

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, 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 [MR 35 #4725], 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 will contain the remaining Chapters 7-9). The individual fascicles of the original French edition have been extensively reviewed [Chs. 1--4, MR 14, 960, 2e édn. MR 36 #2763; Ch. 5, MR 18, 881, 2e edn. MR 35 #322; Ch.6, MR 23 #A2033; Chs. 7-8, MR 31 #3539; Ch. 9, MR 43 #2183]. 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 Chs. 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).Read More