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  • Author or Editor: A. Rényi x
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We prove that if I k are disjoint blocks of positive integers and n k are independent random variables on some probability space (Ω,F,P) such that n k is uniformly distributed on I k , then N 1 / 2 k = 1 N ( sin 2 π n k x E ( sin 2 π n k x ) ) has, with P-probability 1, a mixed Gaussian limit distribution relative to the probability space ((0, 1),B, λ), where B is the Borel σ-algebra and λ is the Lebesgue measure. We also investigate the case when n k have continuous uniform distribution on disjoint intervals I k on the positive axis.

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