{"title":"l<s:1>罗斯级数分母的r-迭代均值的收敛性结果","authors":"R. Giuliano","doi":"10.1515/udt-2016-0020","DOIUrl":null,"url":null,"abstract":"Abstract In the present paper we extend two classic asymptotic results concerning convergence in probability and convergence in distribution for the denominators of the Lüroth series and obtain new theorems concerning the same two kinds of convergence for the r-iterated arithmetic means of such denominators. These results are extended to r-iterated weighted means.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"47 1","pages":"179 - 203"},"PeriodicalIF":0.0000,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Convergence Results for r-Iterated Means of the Denominators of the Lüroth Series\",\"authors\":\"R. Giuliano\",\"doi\":\"10.1515/udt-2016-0020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In the present paper we extend two classic asymptotic results concerning convergence in probability and convergence in distribution for the denominators of the Lüroth series and obtain new theorems concerning the same two kinds of convergence for the r-iterated arithmetic means of such denominators. These results are extended to r-iterated weighted means.\",\"PeriodicalId\":23390,\"journal\":{\"name\":\"Uniform distribution theory\",\"volume\":\"47 1\",\"pages\":\"179 - 203\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Uniform distribution theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/udt-2016-0020\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Uniform distribution theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/udt-2016-0020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Convergence Results for r-Iterated Means of the Denominators of the Lüroth Series
Abstract In the present paper we extend two classic asymptotic results concerning convergence in probability and convergence in distribution for the denominators of the Lüroth series and obtain new theorems concerning the same two kinds of convergence for the r-iterated arithmetic means of such denominators. These results are extended to r-iterated weighted means.
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