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It is easy to see that a finitely generated group is residually amenable if and only if there exists an bi-invariant ultra-metric on $G$ and a finitely additive $G$-invariant measure on open (with respect to the metric) subsets of $G$.
It is easy to see that a group is residually amenable if and only if there exists an bi-invariant ultra-metric on $G$ and a finitely additive $G$-invariant measure on open (with respect to the metric) subsets of $G$.
It is easy to see that a finitely generated group is residually amenable if and only if there exists an bi-invariant ultra-metric on $G$ and a finitely additive $G$-invariant measure on open (with respect to the metric) subsets of $G$.
It is easy to see that a group is residually amenable if and only if there exists an bi-invariant ultra-metric on $G$ and a finitely additive $G$-invariant measure on open (with respect to the metric) subsets of $G$.
