Corollary 1

Tag 08LU, permanent. Cite it as [Bourbaki, Tag 08LU].

Integration, chapter III, § 1. Measures on a locally compact space

— If $\mu$ and $\nu$ are two positive measures on $X$ such that $\mu \leq \nu$ , then $\| \mu \| \leq \| \nu \|$ ; in particular, if $\nu$ is bounded then so is $\mu$ . Indeed, $\| \nu \| = \| \mu \| + \| \nu - \mu \|$ .

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

Cited by

Nothing.

Cites

Nothing.