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This is the sixth and last of the books that form the core of the Bourbaki series, comprising chapters 1-6 in English translation. One striking feature is its exposition of abstract harmonic analysis and the structure of locally compact Abelian groups. This English edition corrects misprints, updates references, and revises the definition of the concept of measurable equivalence relations.

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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.

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