Corollary

Tag 097A, permanent. Cite it as [Bourbaki, Tag 097A].

Integration, chapter V, § 8. Products of measures

— If the measure $\mu$ (resp. $\mu'$ ) is concentrated on $M$ (resp. $M'$ ), then $\mu \otimes \mu'$ is concentrated on $M \times M'$ .

For, $(T \times T') - (M \times M')$ is the union of the sets $(T - M) \times T'$ and $T \times (T' - M')$ , which are locally negligible for $\mu \times \mu'$ by Prop. 4.

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

Cited by

Nothing.

Cites

Prop. 4