Corollary

Tag 08M8, permanent. Cite it as [Bourbaki, Tag 08M8].

Integration, chapter III, § 1. Measures on a locally compact space

— If X is paracompact then the topologies induced on $\mathscr{M}_+(X)$ by the vague topology and the topology of compact convergence coincide.

However, the topologies induced on $\mathscr{M}_+(X)$ by the topology of compact convergence and the topology of strictly compact convergence may be different when X is not paracompact (Exer. 3).

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

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