Definition 3

Tag 093B, permanent. Cite it as [Bourbaki, Tag 093B].

Integration, V, p. 53, § 5. Measures defined by numerical densities

Two complex measures $\theta, \theta'$ on a locally compact space $T$ are said to be equivalent if the measures $|\theta|$ and $|\theta'|$ satisfy the conditions a), b), c) of Prop. 10.

For $\theta$ and $\theta'$ to be equivalent, it is therefore necessary and sufficient that $|\theta|$ and $|\theta'|$ be equivalent.

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

Cited by

Proposition 12, § 5

Cites

Prop. 10