Let $(X,\mathcal B,\mu,T)$ be an ergodic probability-preserving dynamical system, and let $\mathcal P$ be a finite measurable partition of $X$. For $n \in \mathbb N$, let
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\begin{align*}
\mathcal P_0^{n-1}:=\bigvee_{k=0}^{n-1}T^{-k}\mathcal P
\end{align*}
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denote the partition into $n$-names, and let $h:=h_\mu(T,\mathcal P)$.
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For every $\varepsilon>0$, there exist subfamilies $\mathcal W_n(\varepsilon)\subseteq \mathcal P_0^{n-1}$ such that
Moreover, for every $0<\delta<1$ and every $\varepsilon>0$, there exists $N=N(\delta,\varepsilon)\in\mathbb N$ such that for all $n\geq N$, every subfamily $\mathcal V_n\subseteq \mathcal P_0^{n-1}$ satisfying