Let P, P1, P2 be nonempty subsets of E. Then the following hold: (i) The support P is sublinear and closed (i.e. dom P = E). (ii) One support dominates over another if and only if its closed convex hull also dominates over the other, i.e. P1 P2 , if and only if co P1 co P2. (iii) The supports are equal if and only if the closed convex hulls are the same, i.e. P1 = P2 , if and only if co P1 = co P2