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).
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.
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)
