Kamarul Haili, Hailiza
*A Metric Discrepancy Estimate for A Real Sequence.*

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## Abstract

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))1n=1 that for every " > 0, D(N, x) = O(N âˆ’1 2 (logN) 5 2+") 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 + " can be reduced to 3 2 + " in a special case where gn(x) = anx for a sequence of integers (an)1n=1. This paper extends this result to the case where the sequence (an)1n=1 can be assumed to be real. The lighter version of this theorem is also shown in this paper. Keywords Discrepancy, uniform distribution, Lebesgue measure, almost everywhere

Item Type: | Article |
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ID Code: | 2453 |

Deposited By: | Assoc Prof Hazimah Abd Hamid |

Last Modified: | 01 Jun 2010 03:03 |

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