Proposition 2

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

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

— Let $f$ be a mapping of $X$ into a topological space $G$ . For $f$ to be $\nu$ -measurable, it is necessary and sufficient that $f$ be $\lambda_\alpha$ -measurable for every $\alpha \in A$ .

This follows at once from Cor. 2 of Prop. 11 of $§ 1$ .

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

Cited by

Corollary 2, § 2
Proposition 2, § 3
Proposition 6, § 3
Proposition 10, § 8
Proposition 11, § 8
Proposition 2, § 8

Cites

Nothing.