학술논문
Scattered Subsets of Groups.
Document Type
Article
Author
Source
Subject
*BOREL subsets
*GROUP theory
*SUBSPACES (Mathematics)
*TOPOLOGICAL spaces
*MATHEMATICAL proofs
*INVARIANTS (Mathematics)
*MEASURE theory
*INFINITY (Mathematics)
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Language
ISSN
0041-5995
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 ℵ scattered subsets. [ABSTRACT FROM AUTHOR]