Geodesic
Some Remarks on the Moment Problem and Its Relation to the Theory of Extrapolation of Spaces
Matematičeskie zametki, Tome 91 (2012) no. 1, pp. 79-92

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It is well known that that the coincidence of integer moments ($n$th-power moments, where $n$ is an integer) of two nonnegative random variables does not imply the coincidence of their distributions. Moreover, we show that, given coinciding integer moments, the ratio of half-integer moments may tend to infinity arbitrarily fast. Also, in this paper, we give a new proof of uniqueness in the continuous moment problem and show that, in that problem, it is impossible to replace the condition of coincidence of all moments by a two-sided inequality between them, while preserving the inequality between the distributions. In conclusion, we study the relationship with the theory of extrapolation of spaces.
Keywords: nonnegative random variable, distribution function, half-integer moment, continuous moment problem, Orlicz space.
Mots-clés : integer moment, extrapolation of spaces, Lebesgue measure 
K. V. Lykov. Some Remarks on the Moment Problem and Its Relation to the Theory of Extrapolation of Spaces. Matematičeskie zametki, Tome 91 (2012) no. 1, pp. 79-92. http://geodesic.mathdoc.fr/item/MZM_2012_91_1_a7/
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