There exists an absolute constant 
such that for any positive integer 
, the discrepancy of any sequence
satisfies
 |
(Kuipers and Niederreiter 1974, pp. 112-113; Bailey and Crandall 2002).
Erdős-Turán Discrepancy Bound
See also
DiscrepancyExplore with Wolfram|Alpha
References
Bailey, D. H. and Crandall, R. E. "Random Generators and Normal Numbers." Exper. Math. 11, 527-546, 2002.Kuipers, L. and Niederreiter, H. Uniform Distribution of Sequences. New York: Wiley, 1974.Referenced on Wolfram|Alpha
Erdős-Turán Discrepancy BoundCite this as:
Weisstein, Eric W. "Erdős-Turán Discrepancy Bound." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Erdos-TuranDiscrepancyBound.html