Distribution Modulo 1

  • D. P. Parent
Part of the Problem Books in Mathematics book series (PBM)


Let (u n)neN be a sequence of elements in the interval [0,1], and let [α, β] be an interval within [0,1]. For every integer N eN* we denote by sN(α, β) the number of integers k such that 0 ≤ k < N, u k e [α,β]. The DISCREPANCY is the sequence (D N) defined by:
$${D_N} = \mathop {\sup }\limits_{0\alpha \beta 1} \left| {\frac{{{s_N}(\alpha ,\beta )}}{N} - (\beta - \alpha )} \right|.$$


Real Number Haar Measure Trigonometric Polynomial Unique Fixed Point Preceding Argument 
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© Springer Science+Business Media New York 1984

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  • D. P. Parent

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