Bourbaki

Proposition 1

Tag 090I, permanent. Cite it as [Bourbaki, Tag 090I].

Integration, chapter V, § 2. Summable families of positive measures

— Let f be a positive numerical function defined on X. Then

ν∙(f)=∑α∈Aλα∙(f). \nu^\bullet(f) = \sum_{\alpha \in A} \lambda_\alpha^\bullet(f).

This follows at once from Remark 1, Prop. 11 of §1, No. 3 and Prop. 3 of §1, No. 1.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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Cites

Transcribed from the printed volume. Not translated.