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Note on irregularities of distribution
Author(s) -
Beck J.,
Chen W. W. L.
Publication year - 1986
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300013966
Subject(s) - mathematics , distribution (mathematics) , chen , citation , library science , combinatorics , computer science , mathematical analysis , paleontology , biology
Let U K = [0, 1) K be the K -dimensional unit cube, where K ≥ 2. Suppose that we have a distribution ℘ of N points in U K . For × = ( x 1 , … , x K ) e U K , let A ( x ) denote the box and write Note that since N is the cardinality of ℘ and x 1 … x K is the K -dimensional volume of A (x), the term Nx 1 … x K represents the “expected number” of, points of ℘ in A (x).