Corollary 4

Tag 09O0, permanent. Cite it as [Bourbaki, Tag 09O0].

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

If $\mu$ and $\nu$ are two measures on T such that $\mu^* = \nu^*$ , then $\mu = \nu$ .

For, the equality $\mu^* = \nu^*$ implies that $\mu^*(f) = \nu^*(f)$ for every positive function $f$ that is moderated for $\mu$ and $\nu$ , hence for every positive function with compact support; it follows that $\mu^* = \nu^*$ (No. 2, Prop. 2), then $\mu = \nu$ (No. 2, Cor. of Prop. 2).

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

Cited by

Nothing.

Cites

Cor. of Prop. 2
No. 2, Prop. 2