Given a real-valued continuous function ƒ on the half-line [0,∞) we denote by P*(ƒ) the set of all probability measures μ on [0,∞) with finite ƒ-moments (n = 1,2...). A function ƒ is said to have the identification propertyif probability measures from P*(ƒ) are uniquely determined by their ƒ-moments. A function ƒ is said to be a Bernstein function if it is infinitely differentiable on the open half-line (0,∞) and is completely monotone for some nonnegative integer n. The purpose of this paper is to give a necessary and sufficient condition in terms of the representing measures for Bernstein functions to have the identification property.
@article{bwmeta1.element.bwnjournal-article-smv118i2p185bwm,
author = {K. Urbanik},
title = {A characterization of probability measures by f-moments},
journal = {Studia Mathematica},
volume = {119},
year = {1996},
pages = {185-204},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv118i2p185bwm}
}
Urbanik, K. A characterization of probability measures by f-moments. Studia Mathematica, Tome 119 (1996) pp. 185-204. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv118i2p185bwm/
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