Stochastic dominance: A bibliographical rectification and a restatement of Whitmore's theorem (Q1085764)

The aim of this note is to make clear that the fundamental theorem on stochastic dominance of degree two was discovered by \textit{J. Karamata} [''Sur une inégalité relative aux fonctions convexes'', Publ. Math. de l'Univ. de Belgrade 1, 145-148 (1932)]. Apart from this historical rectification, it is interesting to remark that the proof is simple and elegant and can be used to characterize stochastic dominance of any order. We give a simple proof along these lines of Whitmore's theorem about third degree stochastic dominance.