Let Kq be the class of probability distributions on the set of non-negative integer powers of a number q > 1 (^-distributions), P = {p* = />(*), k = 0,1,...} is a distribution from the class Kq which has the moments of all orders. It is shown that in order that the distribution P is uniquely determined in the class K q by the sequence of its moments provided that p* > 0, & = 0,1,..., it is necessary, and under the condition that •
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