Proposition 18

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

— For every sequence $(A_n)$ of subsets of X,

\mu^*\left(\bigcup_n A_n\right) \leq \sum_n \mu^*(A_n).

These propositions are the translations of Props. 10 and 13 and of Th. 3 of No. 3 for characteristic functions of sets.

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

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