Journal of Theoretical Probability

, Volume 20, Issue 3, pp 663–693 | Cite as

The Hausdorff Moment Problem under Finite Additivity

  • Enrique Miranda
  • Gert de Cooman
  • Erik Quaeghebeur

We investigate to what extent finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all finitely additive probability measures with a given moment sequence. Our investigation leads to several elegant expressions for this lower envelope, and it allows us to conclude that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions.


Hausdorff moment problem coherent lower prevision lower distribution function complete monotonicity 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Enrique Miranda
    • 1
  • Gert de Cooman
    • 2
  • Erik Quaeghebeur
    • 2
  1. 1.Deptartment of Statistics and Operations ResearchRey Juan Carlos UniversityMóstolesSpain
  2. 2.Ghent University, Systems Research GroupZwijnaardeBelgium

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