Scattered Subsets of Groups

  • T. O. Banakh
  • I. V. Protasov Kyiv Nat. Taras Shevchenko Univ.
  • 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.
How to Cite
Banakh, T. O., I. V. Protasov, and S. V. Slobodianiuk. “Scattered Subsets of Groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 3, Mar. 2015, pp. 304-12,
Research articles