{"title":"典型贝斯科维奇集与直线的交点","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":"{\"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}","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}
The Intersection of Typical Besicovitch Sets with Lines
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.