Remark 2

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

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

If $T$ is locally compact, then every premeasure $w$ on $T$ is a measure. For, every $x \in T$ admits a compact neighborhood $K$ , and $|w|^*(K) = \|w_K\| < +\infty$ , so that the encumbrance $|w|^*$ is locally bounded.

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

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