Remark 4

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

Integration, IX, p. 45, § 3. Measures and additive set functions

If I is a countably additive and locally bounded function, the preceding remark implies at once that $I(K) < +\infty$ for every compact set $K \subset T$ .

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

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