Abstract
We discuss a uniqueness property of the characteristic function of an absolutely continuous probability measure. Our study is initiated by the question posed by N.G. Ushakov: is it true that, for any interval [a,b]⊂R, 0∉[a,b], there exists a characteristic function f such that f≢e−t2/2, but f(t)=e−t2/2 for all t∈[a,b]?
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