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On strong uniform distribution IV


Let be a strictly increasing sequence of natural numbers and let be a space of Lebesgue measurable functions defined on. Let denote the fractional part of the real number. We say that is an sequence if for each we set, then, almost everywhere with respect to Lebesgue measure. Let. In this paper, we show that if is an for, then there exists such that if denotes,. We also show that for any sequence and any nonconstant integrable function on the interval,, almost everywhere with respect to Lebesgue measure.

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Correspondence to R Nair.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Nair, R. On strong uniform distribution IV. J Inequal Appl 2005, 639193 (2005).

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