Geodesic
On the problem of characterizing probability distributions by absolute moments of~partial sums
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 473-481

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The paper indicates close to necessary conditions sufficient for the unique determination of a symmetric probability distribution by the sequence of absolute moments of sums of independent random variables having this distribution.
Keywords: characteristic function, sums of independent random variables, absolute moments, the Cramer condition, a Cauchy-type integral. 
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     author = {A. I. Il'inskii and G. P. Chistyakov},
     title = {On the problem of characterizing probability distributions by absolute moments of~partial sums},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {473--481},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a2/}
}
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A. I. Il'inskii; G. P. Chistyakov. On the problem of characterizing probability distributions by absolute moments of~partial sums. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 473-481. http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a2/