Elements of mathematics. Integration II: Chapters 7–9. Transl. from the 1963 and 1969 French originals by Sterling K. Berberian. (English) Zbl 1095.28002

Bourbaki, Nicolas

Berlin: Springer (ISBN 3-540-20585-3/hbk). vii, 326 p. (2004).

This is an unchanged translation of the original French editions of 1963 resp. 1969 of Chapters 7 and 8 resp. 9 of N. Bourbaki’s [“Éléments de mathématique, Livre VI, Intégration”. Chapitre 7: Mesure de Haar. Chapitre 8: Convolution et représentations. Hermann, Paris (1963; Zbl 0156.03204), Éléments de mathématique. Fasc. XXXV. Livre VI: Intégration. Chapitre IX: Intégration sur les espaces topologiques séparés, Hermann, Paris (1969; Zbl 0189.14201)], treating Haar measure, convolution, measures on Hausdorff topological spaces, abstract Fourier transform. Accordingly the latest references are from 1967.
For the translation of Vol. 1 see [N. Bourbaki, “Elements of mathematics. Integration. I. Chapters 1–6”, Translated from the 1959, 1965 and 1967 French originals by Sterling K. Berberian, Springer, Berlin (2004; Zbl 1095.28001)].

Reviewer: Hans F. Günzler (Kiel)

MSC:

28-02	Research exposition (monographs, survey articles) pertaining to measure and integration
46-02	Research exposition (monographs, survey articles) pertaining to functional analysis
01A75	Collected or selected works; reprintings or translations of classics
43-02	Research exposition (monographs, survey articles) pertaining to abstract harmonic analysis
28C15	Set functions and measures on topological spaces (regularity of measures, etc.)
28C10	Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
28-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
46-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis

Keywords:

Haar measure; convolution; quotient group; homogeneous space; group representations; measures on Radon space; Fourier transform; topological spaces