TY - JOUR
AU - T. O. Banakh
AU - I. V. Protasov
AU - S. V. Slobodianiuk
PY - 2015/03/25
Y2 - 2022/10/02
TI - Scattered Subsets of Groups
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 67
IS - 3
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1983
AB - 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.
ER -