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Densing Sets

โœ Scribed by D. Berend; M.D. Boshernitzan


Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
492 KB
Volume
115
Category
Article
ISSN
0001-8708

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โœฆ 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


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