arXiv:math/0408115 Abstract

arXiv:math/0408115 [math.GN]Abstract References Reviews Resources

Limits in compact abelian groups

Published 2004-08-09Version 1

Let X be compact abelian group and G its dual (a discrete group). If B is an infinite subset of G, let C_B be the set of all x in X such that <phi(x) : phi \in B> converges to 1. If F is a free filter on G, let D_F be the union of all the C_B for B in F. The sets C_B and D_F are subgroups of X. C_B always has Haar measure 0, while the measure of D_F depends on F. We show that there is a filter F such that D_F has measure 0 but is not contained in any C_B. This generalizes previous results for the special case where X is the circle group.

Comments: 14 pages

Categories: math.GN, math.GR

Subjects: 54H11, 22C05

Keywords: compact abelian group, circle group, discrete group, haar measure, infinite subset

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