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 ...
               
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