2 problems

Let $A,B subseteq ewline mathbb Z$ be nonempty, and let $mathbf F=(Fn){ninmathbb N}$ be a Følner sequence of finite subsets of $mathbb Z$, meaning that … for every $t\in\mathbb Z$.…

Let $(X,\mu,T)$ be a measure-preserving system, and let $\Phi_N=\{1,\dots,N\}$ be the standard Følner sequence in $\mathbb{Z}$. For a fixed positive integer $k$, say that $X$ has p…