Measure density for set decompositions and uniform distribution

TL;DR

This paper extends Buck's measure density to arbitrary subsets of natural numbers using system decompositions, leading to new examples and applications in uniform distribution theory.

Contribution

It introduces a generalized measure density concept for subsets of N based on system decompositions, expanding prior work.

Findings

New examples of measure density for various sets

Applications to uniform distribution theory

Generalization of Buck's measure density

Abstract

The aim of this paper is to extend the concept of measure density introduced by Buck for finite unions of arithmetic progressions, to arbitrary subsets of N defined by a given system of decompositions. This leads to a variety of new examples and to applications to uniform distribution theory.