Abstract
On an arbitrary LCA group G, let a probability measure μ 2 have the property that it is uniquely defined, up to a shift and a central symmetry, by the modulus of its characteristic function. Then, if μ 1 is a probability measure on R whose characteristic function is an entire function of finite order with real zeros, the property mentioned for μ 2 remains valid for μ= μ 1× μ 2 on R×G .
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