Mathematical Notes

, Volume 90, Issue 5–6, pp 920–924 | Cite as

A generalization of the Curtiss theorem for moment generating functions

  • A. L. Yakymiv


The Curtiss theorem deals with the relation between the weak convergence of probability measures on the line and the convergence of theirmoment generating functions in a neighborhood of zero. We present a multidimensional generalization of this result. To this end, we consider arbitrary σ-finite measures whose moment generating functions exist in a domain of multidimensional Euclidean space not necessarily containing zero. We also prove the corresponding converse statement.


probability measure moment generating function Curtiss theorem σ-finite measure analytic function Radon-Nykodym derivative 


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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesSteklovRussia

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