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Exceptional Sets in Uniform Distribution
Published online by Cambridge University Press: 20 January 2009
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Let B be a measurable set of real numbers in (0,1) of Lebesgue measure |B| and let x1, …, xn be real. Then
denotes the number of j (1 ≦j≦n) for which the fractional part {xj}∈B. The discrepancy of x1, …, xn is
where the supremum is taken over all intervals I in [0,1].
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- Copyright © Edinburgh Mathematical Society 1979
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