Milan Paštéka | Searcharxiv

arXiv2022

Metrics on N and the distribution of sequences

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

math.NT↗

arXiv2015

Measure density for set decompositions and uniform distribution

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.

math.CA↗