Proposition 3

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

*For every finite number $\alpha \geq 0$ and every pair of measures $\mu, \nu$ on $\mathbf{T}$ ,

(\alpha \mu)^\bullet = \alpha \mu^\bullet \\ (\mu + \nu)^\bullet = \mu^\bullet + \nu^\bullet.

Moreover, the relation $\mu \leq \nu$ implies $\mu^\bullet \leq \nu^\bullet$ .*

The proof is immediate from the analogous statement in Ch. IV (§1, No. 3, Prop. 15).

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

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