Moment-Preserving Shifts and Stochastic Dominance

Let M_n be the set of signed measures on the line with nonempty finite supports whose first n − 1 moments vanish and which satisfy a specified positivity condition. Let M_n* be the minimum-support measures in M_n. Then M_n is the convex cone spanned by M_n* if n ≤ 3 but not if n ≥ 4.