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 
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     author = {K. V. Lykov},
     title = {Some {Remarks} on the {Moment} {Problem} and {Its} {Relation} to the {Theory} of {Extrapolation} of {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
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     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_1_a7/}
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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/