{"title":"The Family of Central Cantor Sets with Packing Dimension Zero","authors":"P. Nowakowski","doi":"10.2478/tmmp-2021-0001","DOIUrl":null,"url":null,"abstract":"Abstract As in the recent article of M. Balcerzak, T. Filipczak and P. Nowakowski, we identify the family CS of central Cantor subsets of [0, 1] with the Polish space X : = (0, 1)ℕ equipped with the probability product measure µ. We investigate the size of the family P0 of sets in CS with packing dimension zero. We show that P0 is meager and of µ measure zero while it is treated as the corresponding subset of X. We also check possible inclusions between P0 and other subfamilies CS consisting of small sets.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"78 1","pages":"1 - 8"},"PeriodicalIF":0.0000,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tatra Mountains Mathematical Publications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/tmmp-2021-0001","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: 1
Abstract
Abstract As in the recent article of M. Balcerzak, T. Filipczak and P. Nowakowski, we identify the family CS of central Cantor subsets of [0, 1] with the Polish space X : = (0, 1)ℕ equipped with the probability product measure µ. We investigate the size of the family P0 of sets in CS with packing dimension zero. We show that P0 is meager and of µ measure zero while it is treated as the corresponding subset of X. We also check possible inclusions between P0 and other subfamilies CS consisting of small sets.
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