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Amenable subsets of groups
Let $X$ be a subset of a group $G$. We say that $X$ is left amenable with respect to $G$ if there is a function $\mu:\mathcal P(G)\to [0,\infty]$ with the following three properties.
$\mu(A\cup B)=\m …
4
votes
Accepted
Amenable subsets of groups
To establish the right amenability of $X$, we invoke the following proposition, due to J.M. Rosenblatt and appearing as Corollary 1.5 in his paper "A generalization of Følner's condition (Math. … Rosenblatt states the proposition in terms of left amenability; we have repurposed it for right amenability. …