A generalization of Kakutani's splitting procedure

TL;DR

This paper explores uniformly distributed sequences of partitions of [0,1], introduces new families of such sequences, and examines their relationship with classical uniformly distributed sequences of points.

Contribution

It generalizes Kakutani's splitting procedure by constructing new families of uniformly distributed partitions and analyzing their connection to point sequences.

Findings

New families of u.d. partitions constructed

Relations between partitions and point sequences established

Enhanced understanding of distribution properties in [0,1]

Abstract

In this paper we will study uniformly distributed sequences of partitions of [0,1], a concept which has been introduced by Kakutani in 1976. We will construct new families of u.d. sequences of partitions and study relations with the classical concept of uniformly distributed sequences of points.