In mathematics, Dieudonné's theorem, named after Jean Dieudonné, is a theorem on when the Minkowski sum of closed sets is closed.
Statement of theorem
Let nonempty closed convex sets a locally convex space, if either or is locally compact and (where gives the recession cone) is a linear subspace, then is closed.
- ^ J. Dieudonné (1966). "Sur la séparation des ensembles convexes". Math. Ann.. 163.
- ^ Zălinescu, Constantin (2002). Convex analysis in general vector spaces. River Edge, NJ: World Scientific Publishing Co., Inc. pp. 6–7. ISBN 981-238-067-1. MR 1921556.