Limits in compact Abelian groups |
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Authors: | Joan E. Hart Kenneth Kunen |
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Affiliation: | a University of Wisconsin, Oshkosh, WI 54901, USA b University of Wisconsin, Madison, WI 53706, USA |
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Abstract: | For X a compact Abelian group and B an infinite subset of its dual , let CB be the set of all x∈X such that converges to 1. If F is a free filter on , let . 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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Keywords: | primary, 54H11, 22C05 secondary, 43A40 |
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