Proposition 6

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

Integration, VIII, p. 13, § 2. Linear representations of groups

If one equips $\mathscr{M}(X)$ (resp. $\mathscr{C}'(X)$ ) with the topology of uniform convergence in the compact subsets of $\mathscr{K}(X)$ (resp. $\mathscr{C}(X)$ ), then the linear representation $\gamma_\chi$ of $G$ in $\mathscr{M}(X)$ (resp. $\mathscr{C}'(X)$ ) is continuous.

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

Cited by

Proposition 10, § 3

Cites

Nothing.