Additive selections of superadditive set-valued functions

Summary A set-valued functionF from a coneC with a cone-basis of a topological vector spaceX into the family of all non-empty compact convex subsets of a locally convex spaceY is called superadditive provided thatF(x) + F(y) F(x + y), for allx, y C. We show that every superadditive set-valued function admits an additive selection.Dedicated to Professor Otto Haupt on his 100th birthday