Proposition 1

Tag 08CR, permanent. Cite it as [Bourbaki, Tag 08CR].

Functions of a Real Variable, chapter IV, § 2. LINEAR DIFFERENTIAL EQUATIONS

The set $\mathscr{I}$ of integrals of the homogeneous linear equation (4), defined on $J$ , is a vector subspace of the space $C(J; E)$ of continuous maps from $J$ into $E$ .

The proof is immediate.

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

Cited by

Nothing.

Cites

Nothing.