{"title":"绝对友好的措施","authors":"Shreyasi Datta, Justin Liu","doi":"10.1112/mtk.12256","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we extend the work of Pollington and Velani [Selecta Math. 11(2005)] to an <span></span><math></math>-arithmetic set-up, where <span></span><math></math> is a finite set of valuations of <span></span><math></math>. In particular, for an <i>absolutely friendly</i> measure <span></span><math></math> supported on a compact set in <span></span><math></math>, we give a summation condition on an approximating function <span></span><math></math> such that <span></span><math></math> almost no point in the compact set is <span></span><math></math> approximable. The crucial ingredient is a version of the simplex lemma that we prove dynamically.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12256","citationCount":"0","resultStr":"{\"title\":\"On absolutely friendly measures on\",\"authors\":\"Shreyasi Datta, Justin Liu\",\"doi\":\"10.1112/mtk.12256\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we extend the work of Pollington and Velani [Selecta Math. 11(2005)] to an <span></span><math></math>-arithmetic set-up, where <span></span><math></math> is a finite set of valuations of <span></span><math></math>. In particular, for an <i>absolutely friendly</i> measure <span></span><math></math> supported on a compact set in <span></span><math></math>, we give a summation condition on an approximating function <span></span><math></math> such that <span></span><math></math> almost no point in the compact set is <span></span><math></math> approximable. The crucial ingredient is a version of the simplex lemma that we prove dynamically.</p>\",\"PeriodicalId\":18463,\"journal\":{\"name\":\"Mathematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12256\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematika\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12256\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematika","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12256","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we extend the work of Pollington and Velani [Selecta Math. 11(2005)] to an -arithmetic set-up, where is a finite set of valuations of . In particular, for an absolutely friendly measure supported on a compact set in , we give a summation condition on an approximating function such that almost no point in the compact set is approximable. The crucial ingredient is a version of the simplex lemma that we prove dynamically.
期刊介绍：
Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.
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