Remark 3
Tag 08VA, permanent. Cite it as [Bourbaki, Tag 08VA].
Integration, IV, p. 68, § 5. Measurable functions and sets
The hypothesis a) can be replaced by the condition that the inverse image under of every open ball of F is measurable.
The case of numerical functions (finite or not) deserves special mention:
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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