Example 2

Tag 090X, permanent. Cite it as [Bourbaki, Tag 090X].

Integration, chapter V, § 3. Integration of positive measures

The mapping $t \mapsto \varepsilon_t$ of T into $\mathscr{M}_+(T)$ is vaguely continuous, scalarly essentially μ-integrable for every positive measure μ on T, and one has $\int \varepsilon_t\, d\mu(t) = \mu$ .

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

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