On absolutely normal numbers and their discrepancy estimate

02/14/2017

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by   Verónica Becher, et al.

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We construct the base 2 expansion of an absolutely normal real number x so that, for every integer b greater than or equal to 2, the discrepancy modulo 1 of the sequence (b^0 x, b^1 x, b^2 x , ...) is essentially the same as that realized by almost all real numbers.