Proposition 1

Tag 08Q9, permanent. Cite it as [Bourbaki, Tag 08Q9].

Integration, chapter IV, § 2. Negligible functions and sets

— If $f$ is a negligible function $\geq 0$ , then every numerical function $g$ such that $0 \leq g \leq \alpha f$ ( $\alpha$ a scalar $> 0$ ) is negligible. For, $0 \leq |\mu|^*(g) \leq \alpha |\mu|^*(f) = 0$ .

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

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