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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Invariant means on the continuous bounded functions

Author: Joseph Rosenblatt
Journal: Trans. Amer. Math. Soc. 236 (1978), 315-324
MSC: Primary 43A07
MathSciNet review: 0473714
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Abstract: Let G be a noncompact nondiscrete $\sigma$-compact locally compact metric group. A Baire category argument gives measurable sets $\{ {A_\gamma }:\gamma \in \Gamma \}$ of finite measure with card $(\Gamma ) = c$ which are independent on the open sets. One approximates $\{ {A_\gamma }:\gamma \in \Gamma \}$ by arrays of continuous bounded functions with compact support and then scatters these arrays to construct functions $\{ {f_\gamma }:\gamma \in \Gamma \}$ in ${\text {CB}}(G)$ with a certain independence property. If G is also amenable as a discrete group, the existence of these independent functions shows that on ${\text {CB}}(G)$ there are ${2^c}$ mutually singular elements of LIM each of which is singular to TLIM.

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Article copyright: © Copyright 1978 American Mathematical Society