Characterization of Probability Distributions on Locally Compact Abelian Groups Nick J Thorpe arguing that this could lead

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Characterization of Probability Distributions on Locally Compact Abelian Groups Nick J Thorpe arguing that this could leadIt is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac Bernstein theorem, is a typical example of a so called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible