Proposition 12

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

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

— Let $\mu$ be a positive measure on $T$ that belongs to the domain of $\Lambda$ , and let $f$ be a universally measurable function $\geq 0$ defined on $X$ . If $f$ is moderated for the measure $\mu \Lambda$ , or if the measures $\lambda_t$ are bounded, then the function $\Lambda f$ is $\mu$ -measurable and

\langle \mu \Lambda, f \rangle = \langle \mu, \Lambda f \rangle .

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

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Cites

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