Definition 6

Tag 09N4, permanent. Cite it as [Bourbaki, Tag 09N4].

Integration, chapter IX, § 1. Premeasures and measures on a topological space

A function $f \in \mathscr{F}_+$ (resp. a subset A of T) is said to be locally negligible for the measure $\mu$ if $\mu^*(f) = 0$ (resp. $\mu^*(A) = 0$ ). One says that $\mu$ is concentrated on a subset A of T if T − A is locally $\mu$ *-negligible*.

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

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