Paštéka, Milan; Tichy, Robert Measurable sequences. (English) Zbl 1452.11013 Riv. Mat. Univ. Parma (N.S.) 10, No. 1, 63-84 (2019). In the paper numerous interrelations between several notions connected with the distribution of sequences in various structures (real numbers, integers, ring of polyadic numbers) are described, in particular between various variants of the notion of a distribution function. For instance, between asymptotic distribution function from the theory of uniform distribution of sequences and distribution functions of random variables, or connection between independence in the sense of probability theory and statistical independence of sequences in case of continuous distribution functions, etc. The techniques used in the paper employ tools from the theory of the uniform distribution in \(\mathbb{R}\) (H. Weyl) or in \(\mathbb{Z}\) (I. Niven), that from the theory of Buck measure density theory, the asymptotic density, from probabilistic number theory, or the topology of polyadic numbers. Reviewer: Štefan Porubský (Praha) Cited in 3 Documents MSC: 11B05 Density, gaps, topology 11K06 General theory of distribution modulo \(1\) 11K31 Special sequences 11J71 Distribution modulo one 11B25 Arithmetic progressions Keywords:density; distribution function; uniform distribution; Buck measure density: ring of polyadic numbers × Cite Format Result Cite Review PDF Full Text: arXiv Link