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Note on irregularities of distribution

Published online by Cambridge University Press:  26 February 2010

J. Beck  and
W. W. L. Chen
J. Beck
Affiliation:
Eötvös Loránd University, Budapest, Hungary.
W. W. L. Chen
Affiliation:
Imperial College, London, SW7 2BZ.
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Extract

Let UK = [0, 1)K be the K-dimensional unit cube, where K ≥ 2. Suppose that we have a distribution ℘ of N points in UK. For × = ( x1, … , xK) ε UK, let A(x) denote the box

and write

Note that since N is the cardinality of ℘ and x1 … xK is the K-dimensional volume of A(x), the term Nx1 … xK represents the “expected number” of, points of ℘ in A(x).

Type
Research Article
Information
Mathematika , Volume 33 , Issue 1 , June 1986 , pp. 148 - 163
Copyright
Copyright © University College London 1986

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References

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