科研之友
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摘要
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 mu(A) = 0 for each left invariant Banach measure mu on G. It is also shown that every infinite group can be split into a"mu(0) scattered subsets.
- 出版日期2015-8
