Corollary

Tag 092O, permanent. Cite it as [Bourbaki, Tag 092O].

Integration, V, p. 43, § 5. Measures defined by numerical densities

Let $\mathbf{f}$ be a function defined on $T$ , with values in a Banach space $F$ or in $\overline{\mathbf{R}}$ . For $\mathbf{f}$ to be $(u \cdot \theta)$ -measurable, it is necessary and sufficient that $u \mathbf{f}$ be $\theta$ -measurable.

For, $u \mathbf{f}$ is the extension by 0 of $(u \mathbf{f})|S$ to $T$ .

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

Cited by

Proposition 8, § 5
Corollary, § 8

Cites

Nothing.