Corollary 3

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

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

— If the measure $\mu$ is concentrated on a set M, then $\pi(\mu)$ is concentrated on $\pi(M)$ .

For, if $N = X - \pi(M)$ then $\pi^{-1}(N)$ does not intersect M, therefore is locally $\mu$ -negligible, consequently (Cor. 2) N is locally $\nu$ -negligible.

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

Cited by

Corollary, § 6
Corollary 4, § 6
Theorem 1, § 3
§ 2. Quotient of a space by a group; homogeneous spaces
Proposition 5, § 1

Cites

Cor. 2