A note on irregularities of distribution

نویسنده

  • R. L. Graham
چکیده

Let d ≥ 0 be a fixed integer. Suppose X = (x1, x2, x3, . . .) is a sequence in [0, 1) with the property that for every n ≤ N , each of the intervals [ k−1 n , k n ), 1 ≤ k ≤ n, contains at least one xi with 1 ≤ i ≤ n+d. We show that this implies that N = O(d). This is a generalization of a question raised by Steinhaus some 50 years ago.

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تاریخ انتشار 2013