An infinite interval version of the $α$-Kakutani equidistribution problem

Abstract

In this article we extend results of Kakutani, Adler-Flatto, Smilansky and others on the classical α-Kakutani equidistribution result for sequences arising from finite partitions of the interval. In particular, we describe a generalization of the equidistribution result to infinite partitions. In addition, we give discrepancy estimates, extending results of .