A ug 2 00 4 Limits in Compact Abelian Groups ∗
نویسنده
چکیده
For X a compact abelian group and B an infinite subset of its dual X̂, let CB be the set of all x ∈ X such that 〈φ(x) : φ ∈ B〉 converges to 1. If F is a free filter on X̂, let DF = {CB : B ∈ F}. The sets CB and DF are subgroups of X. CB always has Haar measure 0, while the measure of DF depends on F . We show that there is a filter F such that DF has measure 0 but is not contained in any CB . This generalizes previous results for the special case where X is the circle group.
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