# Uniform distribution of sequences

@inproceedings{Kuipers1974UniformDO, title={Uniform distribution of sequences}, author={Lauwerens Kuipers}, year={1974} }

( 1 ) {xn}z= Xn--Z_I Zin-Ztn-I is uniformly distributed mod 1, i.e., if ( 2 ) lim (1/N)A(x, N, {xn}z)-x (0x<_ 1), where A(x, N, {Xn)) denotes the number of indices n, l<=n<=N such that {x} is less than x. The ollowing distribution properties of the sequence (Xn)=(nO)(t an arbitrary positive real number) are well-known" (i) I Z--Zn_c and Z/Zn_xol as n-c, then (Xn) is uniformly distributed mod z (W. J. Le Veque [6]). (ii) If z-z_x is decreasing, then (Xn)is uniformly distributed modz for almost…

## 2,692 Citations

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