Abstract
It is shown, that for the action of a σ-compact group, being amenable as an abstract discrete group, on a locally compact measure space (X, β, μ), μ is not the unique invariant mean. Furthermore, this paper gives a characterisation of probability spaces, having a unique invariant mean for the action of an amenable group.
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Krasa, S. Non uniqueness of invariant means for amenable group actions. Monatshefte für Mathematik 100, 121–125 (1985). https://doi.org/10.1007/BF01295668
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DOI: https://doi.org/10.1007/BF01295668