Corollary 2

Tag 0955, permanent. Cite it as [Bourbaki, Tag 0955].

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

— Let T and X be two locally compact spaces, $(\lambda_i)_{1 \leq i \leq n}$ a finite sequence of positive measures on T, and let $\mu = \sum_{i=1}^n \lambda_i$ . For a mapping $\pi$ of T into X to be $\mu$ -proper, it is necessary and sufficient that it be $\lambda_i$ -proper for every index i, in which case

\sum_{i=1}^n \pi(\lambda_i) = \pi\left( \sum_{i=1}^n \lambda_i \right).

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

Cited by

Definition 2, § 6
Corollary 1, § 6

Cites

Nothing.