{"title":"The Intersection of Typical Besicovitch Sets with Lines","authors":"T. K'atay","doi":"10.14321/REALANALEXCH.45.2.0453","DOIUrl":null,"url":null,"abstract":"We show that a typical Besicovitch set $B$ has intersections of measure zero with every line not contained in it. Moreover, every line in $B$ intersects the union of all the other lines in $B$ in a set of measure zero.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2019-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Real Analysis Exchange","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14321/REALANALEXCH.45.2.0453","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
We show that a typical Besicovitch set $B$ has intersections of measure zero with every line not contained in it. Moreover, every line in $B$ intersects the union of all the other lines in $B$ in a set of measure zero.
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