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