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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 theconcordance 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).
Inhaltsverzeichnis
Haar Measure: Construction of a Haar Measure. Quotient of a Space by a Group; Homogeneous Spaces. Applications and Examples.- Convolution and Representations: Convolution. Linear Representations of Groups. Convolution of Measures on Groups. Convolution of Measures and Functions. The Space of Closed Subgroups.- Measures on Hausdorff Topological Spaces: Premeasures and Measures on a Topological Space. Operations on Measures. Measures and Additive Set Functions. Inverse Limits of Measures. Measures on Completely Regular Space. Promeasures and Measures on a Locally Convex Space.
Zusammenfassung
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 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 theconcordance 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).
Zusatztext
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)
Bericht
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)
