Authors: Berend, D.; Boshernitzan, M.D.
Source: Advances in Mathematics, Volume 115, Number 2, October 1995 , pp. 286-299(14)
Publisher: Academic Press
Abstract:Let ℋ be a family of "large" (in various senses, e.g., of positive Hausdorff dimension or Lebesgue measure) subsets of R. We study sets D of real numbers which are ℋ-densing, namely have the property that, given any set H ∈ ℋ and > 0, there exist an a ∈ for which the set aH is -dense modulo 1. In the special case, where ℋ consists of all subsets of R having a finite accumulations point, ℋ-densing sets are simply Glasner sets, studied earlier.
Document Type: Research Article
Affiliations: Univ Texas, Dept Math, Austin, TX 78712, USA; Rice Univ, Dept Math, Houston, TX 77251, USA and Ben Gurion Univ Negev, Dept Math & Comp Sci, IL 84105 Beer Sheva, Israel
Publication date: 1995-10-01