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The paper contains the mathematical analysis of the so-called Benford's Empirical Law, closely related to the famous Weil's theorem about uniform distribution on [0,1] of the sequence of the fractional parts xn = {nα}, α is an irrational number, and Poincaré theorem about convolutions of the measures on the group S1 = [0, 1)mod 1 . We prove that the Weil's theorem is "robust" in appropriate sense and generalize the Poincaré theorem for the class of dependent random variables.
Published Online: 2004-09-01
Published in Print: 2004-09-01
Copyright 2003, Walter de Gruyter