Corollary 5

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

For every sequence $(A_n)$ of pairwise disjoint measurable sets,

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

This follows from Cor. 4 applied to the $\varphi_{A_n}$ .

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

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