Integration I: Chapters 1-6

ISBN-13: 9783642639302 / Angielski / Miękka / 2012 / 472 str.

N. Bourbaki; Sterling 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 present volume comprises Chapters 1-6 in English translation (a second volume will contain the remaining Chapters 7-9). The individual fascicles of the original French edition have been extensively reviewed. 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 Chs. 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)."

Spis treści

Inequalities of convexity.- Historical Note.- Riesz spaces.- Measures on locally compact spaces.- Extension of a measure. LP spaces.- Integration of measures.- Historical Note.- Vectorial integration.- Historical Note.