%0 Journal Article
%T A Metric Discrepancy Estimate for A Real Sequence
%A Hailiza Kamarul Haili
%J Matematika
%D 2006
%I Universiti Teknologi Malaysia
%X A general metrical result of discrepancy estimate related to uniform distribution is proved in this paper. It has been proven by J.W.S Cassel and P.Erdos & Koksma in [2] under a general hypothesis of (gn(x))£¤n=1 that for every ¦Å > 0,                      D(N, x) = O(N-  (log N)5/2+¦Å) for almost all x with respect to Lebesgue measure. This discrepancy estimate was improved by R.C. Baker [5] who showed that the exponent 5/2+¦Å can be reduced to 3/2+¦Å in a special case where gn(x) = anx for a sequence of integers (an)£¤n=1. This paper extends this result to the case where the sequence (an)£¤n=1 can be assumed to be real. The lighter version of this theorem is also shown in this paper.
%K Discrepancy
%K uniform distribution
%K Lebesgue measure
%K almost everywhere.
%U http://www.fs.utm.my/matematika/images/stories/matematika/20062213.pdf