An infinite interval version of the α-Kakutani equidistribution problem

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 Drmota–Infusino [8].