## Invariant means on the continuous bounded functions

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- by Joseph Rosenblatt PDF
- Trans. Amer. Math. Soc.
**236**(1978), 315-324 Request permission

## 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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## Additional Information

- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**236**(1978), 315-324 - MSC: Primary 43A07
- DOI: https://doi.org/10.1090/S0002-9947-1978-0473714-8
- MathSciNet review: 0473714