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IRREGULARITIES OF POINT DISTRIBUTION RELATIVE TO CONVEX POLYGONS III

Published online by Cambridge University Press:  01 October 1997

J. BECK  and
W. W. L. CHEN
J. BECK
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, USA
W. W. L. CHEN
Affiliation:
Department of Mathematics, Macquarie University, Sydney, New South Wales 2109, Australia
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Abstract

Suppose that [Pscr ] is a distribution of N points in the unit square U=[0, 1]2. For every x=(x1, x2)∈U, let B(x)=[0, x1]×[0, x2] denote the aligned rectangle containing all points y=(y1, y2)∈U satisfying 0[les ]y1[les ]x1 and 0[les ]y2[les ]x2. Denote by Z[[Pscr ]; B(x)] the number of points of [Pscr ] that lie in B(x), and consider the discrepancy function

D[[Pscr ]; B(x)]=Z[[Pscr ]; B(x)]−Nμ(B(x)),

where μ denotes the usual area measure.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 56 , Issue 2 , October 1997 , pp. 222 - 230
Copyright
The London Mathematical Society 1997

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