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Let $G$ be a countable amenable group with a (left) Følner sequence $(F_n)$. Let $\Gamma$ be a subset of $G$ that has density $1$ with respect to $(F_n)$, in the sense that $$ \lim_{n \to \infty} \...

Let $G$ be an amenable group (so locally compact Hausdorff) and also assume it is second countable if needed. My question is that what are the standard ways (across literature) of defining the upper ...