Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T05:14:39.267Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)