Corollary

Tag 094X, permanent. Cite it as [Bourbaki, Tag 094X].

Integration, chapter V, § 6. Images of a measure

— For a subset A of X to be $\nu$ -measurable, is is necessary and sufficient that $\pi^{-1}(A)$ be $\mu$ -measurable.

However, the image under $\pi$ of a $\mu$ -measurable subset M of T is not necessarily $\nu$ -measurable, even if $\pi$ is continuous and M is $\mu$ -negligible (Exer. 7 and §8, Exer. 1).

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

Cited by

Theorem 4, § 3

Cites

Nothing.