A generalization of the Curtiss theorem for moment generating functions
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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.
Keywordsprobability measure moment generating function Curtiss theorem σ-finite measure analytic function Radon-Nykodym derivative
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