Remark 2

Tag 09NV, permanent. Cite it as [Bourbaki, Tag 09NV].

Integration, chapter IX, § 1. Premeasures and measures on a topological space

Beware, however, that the existence of a sequence of Borel sets of finite measure for $\mu$ , with union T, does not necessarily imply the existence of a sequence of open sets of finite measure with union T (in other words, does not imply that $\mu$ is moderated). See Exer. 8.

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

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