{"title":"On structure of the family of regularly distributed sets with respect to the union","authors":"Szilárd Svitek, Miklós Vontszemű","doi":"10.33039/ami.2021.10.001","DOIUrl":null,"url":null,"abstract":"Let 0 ≤ 𝑞 ≤ 1 and N denotes the set of all positive integers. In this paper we will be interested in 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 study the structure of this family with respect to the union.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematicae et Informaticae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33039/ami.2021.10.001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let 0 ≤ 𝑞 ≤ 1 and N denotes the set of all positive integers. In this paper we will be interested in 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 study the structure of this family with respect to the union.
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