Remarks on the tail order on moment sequences

We consider positively supported Borel measures for which all moments exist. On the set of compactly in this class a partial order is defined via eventual dominance moment sequences. Special classes are identified on total, but it shown that already distributions with smooth densities not total. In particular we construct pair density infinitely many agree and another one alternate often. This disproves some recently published claims to contrary. Some consequences games distributional payoffs discussed.