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Irregularities of point distribution relative to convex polygons II

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  26 February 2010

J. Beck  and
W. W. L. Chen
J. Beck
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903U.S.A..
W. W. L. Chen
Affiliation:
School of MPCE, Macquarie University, Sydney, NSW 2109, Australia.
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Extract

Suppose that is a distribution of N points in the unit square U = [0, 1]2. For every measurable set B in U, let Z[; B] denote the number of ponts of in B, and write

where µ denotes the usual measure in ℝ2

MSC classification

Secondary: 11K38: Irregularities of distribution, discrepancy
Type
Research Article
Information
Mathematika , Volume 40 , Issue 1 , June 1993 , pp. 127 - 136
Copyright
Copyright © University College London 1993

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References

1.Beck, J.. Irregularities of distribution I. Ada Math., 159 (1987), 1–49.Google Scholar
2.Beck, J. and Chen, W. W. L.. Note on irregularities of distribution II. Proc. London Math. Soc, 61 (1990), 251–272.CrossRefGoogle Scholar
3.Beck, J. and Chen, W. W. L.. Irregularities of point distribution relative to half-planes I. Mathematika, 40 (1993), 102–126.Google Scholar
4.Roth, K. F.. On irregularities of distribution III. Ada Arith., 35 (1979), 373–384.Google Scholar