A von Neumann theorem for uniformly distributed sequences of partitions

TL;DR

This paper extends von Neumann's theorem to permutations of sequences of partitions, showing a new connection between dense sequences and uniformly distributed partitions.

Contribution

It introduces a novel theorem that parallels von Neumann's result, applying it to permutations of sequences of partitions.

Findings

Permutation of sequences of partitions can preserve uniform distribution.

The theorem generalizes classical results on dense sequences.

New conditions for uniform distribution in partition sequences.

Abstract

In this paper we consider permutations of sequences of partitions, obtaining a result which parallels von Neumann's theorem on permutations of dense sequences and uniformly distributed sequences of points.