Scattered Subsets of Groups
Banakh, T. O. · Protasov, I. V. · Slobodianiuk, S. V.
Original · EN
We define the scattered subsets of a group as asymptotic counterparts of scattered subspaces of a topological space, and prove that a subset A of a group G is scattered if and only if A contains no 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.
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