Remark
Tag 093C, permanent. Cite it as [Bourbaki, Tag 093C].
Integration, chapter V, § 5. Measures defined by numerical densities
— If and are two equivalent positive measures then the measurable functions defined on , with values in any topological space , are the same for and , as follows at once from Prop. 4 of No. 3.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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