Corollary 1

Tag 0954, permanent. Cite it as [Bourbaki, Tag 0954].

Integration, chapter V, § 6. Images of a measure

— Let $(\mu_\alpha)_{\alpha \in A}$ be a summable family of positive measures on T, such that $\mu = \sum_{\alpha \in A} \mu_\alpha$ ; for a mapping $\pi$ of T into a locally compact space X to be $\mu$ -proper, it is necessary and sufficient that it be $\mu_\alpha$ -proper for every $\alpha \in A$ , and that the family $(\pi(\mu_\alpha))_{\alpha \in A}$ be summable. In this case,

\pi(\mu) = \sum_{\alpha \in A} \pi(\mu_\alpha).

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

Cited by

Definition 1, § 1

Cites

Nothing.