Scattered Subsets of Groups

  • T. O. Banakh
  • I. V. Protasov Kyiv Nat. Taras Shevchenko Univ.
  • S. V. Slobodianiuk

Abstract

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.
Published
25.03.2015
How to Cite
BanakhT. O., ProtasovI. V., and SlobodianiukS. V. “Scattered Subsets of Groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 3, Mar. 2015, pp. 304-12, http://umj.imath.kiev.ua/index.php/umj/article/view/1983.
Section
Research articles