Corollary

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

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

Suppose F is semi-reflexive, and let f be a scalarly essentially $\mu$ -integrable mapping of T into F such that, for every compact subset K of T, $f(K)$ is bounded. Then $\int f d\mu$ belongs to F.

For, every bounded subset of F is relatively weakly compact (TVS, IV, §2, No. 2, Th. 1), and $F = F''$ .

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

Cited by

Proposition 10, § 1

Cites

IV, §2, No. 2, Th. 1