Remarks on the tail order on moment sequences

Vincent Bürgin, Jeremias Epperlein, Fabian Wirth

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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

Original languageEnglish
Article number126135
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - 1 Aug 2022
Externally publishedYes


  • Distribution-valued games
  • Moment sequences
  • Müntz-Szász theorem
  • Stochastic orders
  • Tail order

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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