Corollary 2

Tag 091K, permanent. Cite it as [Bourbaki, Tag 091K].

Integration, chapter V, § 3. Integration of positive measures

— Suppose that $\mu$ is the sum of a summable family $(\mu_\alpha)_{\alpha \in A}$ of positive measures belonging to the domain of $\Lambda$ . For $\mu$ to belong to the domain of $\Lambda$ , it is necessary and sufficient that the family of measures $\mu_\alpha \Lambda$ be summable, in which case $\mu \Lambda = \sum_{\alpha \in A} \mu_\alpha \Lambda$ .

It suffices to apply the Corollary of Prop. 1 of No. 1.

Proposition 5, expressed in the language of diffusions, takes the following form:

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

Cited by

Nothing.

Cites

Corollary of Prop. 1
Proposition 5