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On irregularities of distribution

Published online by Cambridge University Press:  26 February 2010

W. W. L. Chen
W. W. L. Chen
Affiliation:
Imperial collegeLondon, SW7.
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Extract

Let U0 = [(0, 1); and U1 = (0,1)]. Suppose we have a distribution of N points in , where, for k ≥ 1, is the unit cube consisting of the points y = (y1, … , yk+1) with 0 ≤ yi < 1 (i = 1 , … , k + 1). For X = (x1 ,…, xk + 1) in , let B(x) denote the box consisting of all y such that 0 ≤ yi < xi (i = 1 ,…, k + 1), and let denote the number of points of which lie in B(x).

Type
Research Article
Information
Mathematika , Volume 27 , Issue 2 , December 1980 , pp. 153 - 170
Copyright
Copyright © University College London 1980

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References

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