Let $(X,\mathcal{B},\mu)$ be a probability space, let $T:X\to X$ be a measurable measure-preserving map, meaning that $\mu(T^{-1}E)=\mu(E)$ for every $E\in\mathcal{B}$, and let $\alpha$ be a finite measurable partition of $X$. For each $n\in\mathbb{N}$, define the finite measurable partition