Densing Sets

✍ Scribed by D. Berend; M.D. Boshernitzan

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 492 KB
• Volume: 115
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1995.1058

✦ Synopsis

Let (\mathscr{H}) be a family of "large" (in various senses, c.g. of positive Hausdorff dimension or Lebesgue measure) subsets of (\mathbf{R}). We study sets (D) of real numbers which are (\mathscr{H})-densing. namely have the property that, given any set (H \in \mathscr{H}) and (\varepsilon>0), there exist an (a \in \sim) for which the set (a I) is (\varepsilon)-dense modulo 1 . In the special case, where # consists of all subsets of (\mathbf{R}) having a linite accumulations point, (\mathscr{H})-densing sets are simply Glasner sets, studied earlier. ' 1945 Acadenic P'ress. Inc