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On the intersections of exceptional sets in Borel’s normal number theorem and Erdös–Rényi limit theorem

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For any x ∈ [0, 1), let Sn(x) be the partial summation of the first n digits in the binary expansion of x and Rn(x) be its run-length function. The… Click to show full abstract

For any x ∈ [0, 1), let Sn(x) be the partial summation of the first n digits in the binary expansion of x and Rn(x) be its run-length function. The classical Borel’s normal number theorem tells us ...

Keywords: normal number; theorem; number; borel normal; number theorem; intersections exceptional

Journal Title: International Journal of Number Theory
Year Published: 2020

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