  Holroyd and Propp used Hall's marriage theorem to show that, given a
probability distribution pi on a finite set S, there exists an infinite
sequence s_1,s_2,... in S such that for all integers k >= 1 and all s in S, the
number of i in [1,k] with s_i = s differs from k pi(s) by at most 1. We prove a
generalization of this result using a simple explicit algorithm. A special case
of this algorithm yields an extension of Holroyd and Propp's result to the case
of discrete probability distributions on infinite sets.
