Ukrainian Mathematical Journal

, Volume 67, Issue 3, pp 347–356 | Cite as

Scattered Subsets of Groups

  • T. O. Banakh
  • I. V. Protasov
  • S. V. Slobodianiuk

We define scattered subsets of a group as asymptotic counterparts of the scattered subspaces of a topological space and prove that a subset A of a group G is scattered if and only if A does not contain any piecewise shifted IP -subsets. For an amenable group G and a scattered subspace A of G, we show that μ(A) = 0 for each left invariant Banach measure μ on G. It is also shown that every infinite group can be split into ℵ0 scattered subsets.


Cayley Graph Amenable Group Countable Group Injective Sequence Geodesic Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • T. O. Banakh
    • 1
  • I. V. Protasov
    • 2
  • S. V. Slobodianiuk
    • 2
  1. 1.Franko Lviv National UniversityLvivUkraine
  2. 2.Shevchenko Kyiv National UniversityKyivUkraine

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