On the entropy of processes generated by quasifactors

Let $(X,T)$ be a topological dynamical system having the Small Boundary Property and let $μ$ be an ergodic $T$-invariant Borel probability measure on $X$. In this work we show that, if $h_μ(T)>0$, then $h_{\widetildeμ}(\widetilde{T})>0$ for every ergodic quasifactor $\widetildeμ$ of $μ$ having full-