Bourbaki Integration II

Chapters 7–9
Erscheinungsjahr 2013
ISBN: 978-3-662-07931-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 326 Seiten, eBook

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).

Zielgruppe

Research

Autoren/Hrsg.

Bourbaki, N.

Weitere Mitwirkende

Berberian, Sterling K.

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.