Remark 1

Tag 09IG, permanent. Cite it as [Bourbaki, Tag 09IG].

Integration, VIII, p. 9, § 2. Linear representations of groups

To say that $U$ is separately continuous means that $s \mapsto U(s)$ is a continuous mapping of $G$ into the space $\mathscr{L}(E; E)$ of continuous endomorphisms of $E$ , equipped with the topology of pointwise convergence.

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

Cited by

Proposition 1, § 2

Cites

Nothing.