An infinite interval version of the {\alpha}-Kakutani equidistribution problem

TL;DR

This paper generalizes the classical lpha-Kakutani equidistribution theorem to infinite partitions of the interval, providing new discrepancy estimates and extending prior finite partition results.

Contribution

It introduces a novel infinite partition framework for lpha-Kakutani equidistribution, expanding the scope of previous finite partition analyses.

Findings

Extended equidistribution results to infinite partitions.

Provided discrepancy estimates for the generalized sequences.

Built upon and extended prior finite partition results.

Abstract

In this article we extend results of Kakutani, Adler-Flatto, Smilansky and others on the classical $\alpha$-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.