Proposition 2

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

— The sum and upper envelope of a sequence $(f_n)$ of negligible functions $\geq 0$ are negligible.

For, $|\mu|^*(\sum_n f_n) \leq \sum_n |\mu|^*(f_n) = 0$ (§ 1, No. 3, Prop. 13) and $\sup_n f_n \leq \sum_n f_n$ .

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

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