Corollary

Tag 096L, permanent. Cite it as [Bourbaki, Tag 096L].

— Let $(\mu_i)_{i \in I}$ be a summable family of positive measures on T, with sum μ. The family of induced measures $\mu_i|X$ is then summable, and

\sum_{i \in I} (\mu_i|X) = \mu|X.

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

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