A Theorem About Uniform Distribution
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Many problems of combinatorial number theory can be formulated in terms of behavior of orbits of certain transformations acting on the spaces of integers or their subsets. Their analysis can be reduced to problems embracing number theory, probability theory and dynamical systems. In this paper we consider one such question originated from the famous (3x+1)-problem, which illustrates the difficulties which sometimes arise. The main theorem gives the limiting uniform distribution of certain functionals of independent random variables.
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