Characteristics of distributions of sets and their (R)- and (N)-denseness

2022/10/21 by Piotr Miska, Miska, Piotr, János T. Tóth +1
Mathematics · #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2210.12303

openalex publication_date 2022/10/21 · openalex created_date 2022/10/31 · openalex updated_date 2026/07/28

Abstract

Let 0≤ q≤1 and ℕ denotes the set of all positive integers. In this paper we will deal with it too the family U(x^q) of all regularly distributed set X ⊂ ℕ whose ratio block sequence is asymptotically distributed with distribution function g(x) = x^q; x ∈(0,1], and we will show that the regular distributed set, regular sequences, regular variation at infinity are equivalent notations. In this paper also we discuss the relation ship between notations as (N)-denseness, directions sets, generalized ratio sets, dispersion of sequence and exponent of convergence.

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