The distribution of the sequence {<i>n</i>ξ}(<i>n</i> = 0, 1, 2, …)

Abstract

Introduction and statement of results . We shall describe how, for successive integers N , the points { n ξ}, with n = 0, 1, …, N – 1, are distributed in the closed unit interval U = [0, 1]; by showing how successive points { N ξ,} modify the partition of U produced by the previous points. The simple generalization to the k -dimensional sequence { n ξ} = ({ n ξ (1) },{ n ξ (2) }, …,{ n ξ (k) }), in the unit hypercube U k , is also made.