Proposition 13
Tag 09NS, permanent. Cite it as [Bourbaki, Tag 09NS].
Integration, chapter IX, § 1. Premeasures and measures on a topological space
For every subset of , is the infimum of the outer measures of the open sets containing .
The proof is identical to that of Prop. 19 of Ch. IV, §1, No. 4.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.