Remark 1

Tag 098G, permanent. Cite it as [Bourbaki, Tag 098G].

Integration, chapter VI, § 1. Integration of vector-valued functions

If F is finite-dimensional, then every scalarly essentially integrable mapping of T into F is essentially integrable (Ch. V, §1, No. 3). However, in the general case, a scalarly negligible function on a compact space T may even fail to be $\mu$ -measurable (Exer. 12).

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

Cited by

Nothing.

Cites

V, §1, No. 3