Geodesic
A Generalization of the Curtiss Theorem for Moment Generating Functions
Matematičeskie zametki, Tome 90 (2011) no. 6, pp. 947-952

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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 their moment generating functions in a neighborhood of zero. We present a multidimensional generalization of this result. To this end, we consider arbitrary $\sigma$-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.
Keywords: probability measure, moment generating function, Curtiss theorem, $\sigma$-finite measure, analytic function. Radon–Nykodym derivative. 
@article{MZM_2011_90_6_a9,
     author = {A. L. Yakymiv},
     title = {A {Generalization} of the {Curtiss} {Theorem} for {Moment} {Generating} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {947--952},
     publisher = {mathdoc},
     volume = {90},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_6_a9/}
}
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A. L. Yakymiv. A Generalization of the Curtiss Theorem for Moment Generating Functions. Matematičeskie zametki, Tome 90 (2011) no. 6, pp. 947-952. http://geodesic.mathdoc.fr/item/MZM_2011_90_6_a9/