{"title":"不规则Cantor集Ce([0,1])和Cπ([0,1])，以及Cantor- Lebesgue不规则函数Ge和Gπ","authors":"Mykola Yaremenko","doi":"10.37394/232020.2023.3.5","DOIUrl":null,"url":null,"abstract":"In this article, we introduce and study a new class of perfect nowhere-dense sets, which are not selfsimilar in any subset, also, we constructed the correspondent singular functions. We construct a twodimensional irregular Cantor set Ce,π ([0, 1]) on the real plane.","PeriodicalId":93382,"journal":{"name":"The international journal of evidence & proof","volume":"111 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The irregular Cantor sets Ce ([0, 1]) and Cπ ([0, 1]), and the Cantor- Lebesgue irregular functions Ge and Gπ\",\"authors\":\"Mykola Yaremenko\",\"doi\":\"10.37394/232020.2023.3.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we introduce and study a new class of perfect nowhere-dense sets, which are not selfsimilar in any subset, also, we constructed the correspondent singular functions. We construct a twodimensional irregular Cantor set Ce,π ([0, 1]) on the real plane.\",\"PeriodicalId\":93382,\"journal\":{\"name\":\"The international journal of evidence & proof\",\"volume\":\"111 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The international journal of evidence & proof\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/232020.2023.3.5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The international journal of evidence & proof","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/232020.2023.3.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The irregular Cantor sets Ce ([0, 1]) and Cπ ([0, 1]), and the Cantor- Lebesgue irregular functions Ge and Gπ
In this article, we introduce and study a new class of perfect nowhere-dense sets, which are not selfsimilar in any subset, also, we constructed the correspondent singular functions. We construct a twodimensional irregular Cantor set Ce,π ([0, 1]) on the real plane.
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