Integration II: Chapters 7-9

ISBN-13: 9783540205852 / Angielski / Twarda / 2004 / 326 str.

Nicolas Bourbaki; N. Bourbaki; S. K. Berberian

Opis

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 Theories 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)."

Recenzje

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)

Spis treści

VII. — Haar measure.- VIII. — Convolution and representations.- IX. — Measures on Hausdorff topological spaces.- Index of notations.- Index of terminology.- Principal formulas of Chapter VII.- Conditions sufficient for the existence of the convolution product.