Dieudonné's theorem

In mathematics, Dieudonné's theorem, named after Jean Dieudonné, is a theorem on when the Minkowski sum of closed sets is closed.

Statement

Let $X$ be a locally convex space and $A,B\subset X$ nonempty closed convex sets. If either $A$ or $B$ is locally compact and $\mathrm{recc}(A)\cap \mathrm{recc}(B)$ (where $\mathrm{recc}$ gives the recession cone) is a linear subspace, then $A-B$ is closed.