Metrics on N and the distribution of sequences
Number Theory
2022-06-01 v1
Abstract
In the first part of this paper the notion of natural metric on the set of natural numbers is defined. It is such metric that the completion of N is a compact metric space that a probability borel measure exists in order that the sequence {n} is uniformly distributed. A necessary and sufficient condition where a given metric is natural. Later we study the properties of sequences uniformly continuous with respect to given natural metric. Inter alia Theorems 5 and 8 characterise the continuity of distribution function
Keywords
Cite
@article{arxiv.2205.15365,
title = {Metrics on N and the distribution of sequences},
author = {Milan Paštéka},
journal= {arXiv preprint arXiv:2205.15365},
year = {2022}
}