Proposition 8

Tag 09NJ, permanent. Cite it as [Bourbaki, Tag 09NJ].

Integration, chapter IX, § 1. Premeasures and measures on a topological space

Let $\mu$ be the sum of a summable family $(\mu_i)_{i \in I}$ of measures on T. In order that a mapping f of T into a topological space F (Hausdorff or not) be $\mu$ -measurable, it is necessary and sufficient that f be $\mu_i$ -measurable for every $i \in I$ .

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

Cited by

Proposition 5, § 1
Proposition 9, § 1
Lemma 1, § 2
Proposition 5, § 2

Cites

Nothing.