Corollary

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

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

If A and B are two vaguely closed subsets of $\mathscr{M}_+(X)$ , then $A + B$ is vaguely closed in $\mathscr{M}_+(X)$ (hence also in $\mathscr{M}(X; \mathbf{C})$ ).

This is in fact a general property of weakly complete, proper cones in locally convex spaces (TVS, II, §6, No. 8, Cor. 2 of Prop. 11).

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

Cited by

Nothing.

Cites

Prop. 11