The distribution of the sequence {nξ}(n = 0, 1, 2, …)

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