Corollary 1

Tag 0873, permanent. Cite it as [Bourbaki, Tag 0873].

Functions of a Real Variable, chapter II, § 1. PRIMITIVES AND INTEGRALS

The set $\mathscr{H}$ of maps from I into E which admit a primitive on an interval I is a closed (and so complete) vector subspace of the complete vector space $\mathscr{F}_c(I; E)$ of maps from I into E, endowed with the topology of uniform convergence on every compact subset of I (Gen. Top., X, p. 277).

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

Cited by

Corollary 2, § 1

Cites

Nothing.