Corollary

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

If $(A_n)$ is a decreasing sequence of integrable sets, then $\mu(\bigcap_n A_n) = \lim_{n \to \infty} \mu(A_n)$ .

For, if $A = \bigcap_n A_n$ then $\varphi_A$ is the lower envelope of the decreasing sequence $(\varphi_{A_n})$ (No. 3, Prop. 4).

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

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