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Irregularities of point distribution relative to half-planes I

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 08903, U.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 U0, the closed disc of unit area and centred at the origin 0. For every measurable set B in ℝ2, 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. 102 - 126
Copyright
Copyright © University College London 1993

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References

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