A Law of the Iterated Logarithm for General Lacunary Series
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چکیده
This was first proved for Bernoulli random variables by Khintchine. Salem and Zygmund [SZ2] considered the case when the Xk are replaced by functions ak cosnkx on [−π, π] and gave an upper bound ( ≤ 1) result; this was extended to the full upper and lower bound by Erdös and Gál [EG]. Takahashi [T1] extends the result of Salem and Zygmund: Consider a real measurable function f satisfying f(x + 1) = f(x), ∫ 1 0 f(x)dx = 0, and suppose nk is a lacunary sequence of integers, that is, there is a number q so that
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تاریخ انتشار 2012