{"title":"c-均匀分布函数模差的最优下界","authors":"Michael Drmota","doi":"10.1016/1385-7258(88)90004-2","DOIUrl":null,"url":null,"abstract":"<div><p>It is proved that a lower bound for the discrepancy <em>D</em><sub><em>T</em></sub>(<em>ω</em>) of a continuous function <em>ω</em>(<em>t</em>) modulo 1 is given by <em>ϕ</em>(<em>s</em>(<em>T</em>)) infinitely often, where <em>ϕ</em>(<em>x</em>) is integrable on [0, ∞). This bound is best possible in the one dimensional case. Furthermore a generalization to compact, metric spaces is given.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 1","pages":"Pages 21-28"},"PeriodicalIF":0.0000,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(88)90004-2","citationCount":"1","resultStr":"{\"title\":\"An optimal lower bound for the discrepancy of c-uniformly distributed functions modulo\",\"authors\":\"Michael Drmota\",\"doi\":\"10.1016/1385-7258(88)90004-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>It is proved that a lower bound for the discrepancy <em>D</em><sub><em>T</em></sub>(<em>ω</em>) of a continuous function <em>ω</em>(<em>t</em>) modulo 1 is given by <em>ϕ</em>(<em>s</em>(<em>T</em>)) infinitely often, where <em>ϕ</em>(<em>x</em>) is integrable on [0, ∞). This bound is best possible in the one dimensional case. Furthermore a generalization to compact, metric spaces is given.</p></div>\",\"PeriodicalId\":100664,\"journal\":{\"name\":\"Indagationes Mathematicae (Proceedings)\",\"volume\":\"91 1\",\"pages\":\"Pages 21-28\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/1385-7258(88)90004-2\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae (Proceedings)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/1385725888900042\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/1385725888900042","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An optimal lower bound for the discrepancy of c-uniformly distributed functions modulo
It is proved that a lower bound for the discrepancy DT(ω) of a continuous function ω(t) modulo 1 is given by ϕ(s(T)) infinitely often, where ϕ(x) is integrable on [0, ∞). This bound is best possible in the one dimensional case. Furthermore a generalization to compact, metric spaces is given.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
