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arXiv · 2205.15365

Metrics on N and the distribution of sequences

Milan Paštéka
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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

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Milan Paštéka. 2022-05-30. Metrics on N and the distribution of sequences. https://arxiv.org/abs/2205.15365

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