![Cover image for Integration II : chapters 7-9 Cover image for Integration II : chapters 7-9](/client/assets/5.0.0/ctx//client/images/no_image.png)
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000004598789 | QA308 B68 2004 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
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 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).
Author Notes
Nicolas Bourbaki is the pseudonym for a group of mathematicians that included Henri Cartan, Claude Chevalley, Jean Dieudonne, and Andres Weil. Mostly French, they emphasized an axiomatic and abstract treatment on all aspects of modern mathematics in Elements de mathematique. The first volume of Elements appeared in 1939. Subsequently, a wide variety of topics have been covered, including works on set theory, algebra, general topology, functions of a real variable, topological vector spaces, and integration. One of the goals of the Bourbaki series is to make the logical structure of mathematical concepts as transparent and intelligible as possible. The books listed below are typical of volumes written in the Bourbaki spirit and now available in English. (Bowker Author Biography)
Table of Contents
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 |