Let $(X,\mathcal B_X,\mu,T)$ and $(Y,\mathcal B_Y,\nu,S)$ be probability-preserving dynamical systems. Suppose $(Y,\mathcal B_Y,\nu,S)$ is a factor of $(X,\mathcal B_X,\mu,T)$ through a measurable map $\pi:X\to Y$, meaning that $\pi_*\mu=\nu$ and
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\begin{align*}
\pi\circ T = S\circ \pi
\end{align*}
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$\mu$-almost everywhere. Then the Kolmogorov-Sinai entropies satisfy