Definition 8

Tag 08W0, permanent. Cite it as [Bourbaki, Tag 08W0].

Integration, IV, p. 79, § 5. Measurable functions and sets

Let $X$ be a locally compact space, $\mu$ a measure on $X$ , and $A$ a $\mu$ -measurable subset of $X$ . A mapping $f$ of $A$ into a topological space $F$ is said to be $\mu$ -measurable if it satisfies the equivalent conditions of Prop. 15.

If $A$ is locally $\mu$ -negligible, then every mapping of $A$ into $F$ is therefore $\mu$ -measurable.

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

Cited by

§ 5. Measurable functions and sets

Cites

Prop. 15