On the entropy of processes generated by quasifactors

Given a measurable dynamical system $(X,\mathcal{X},\mu,T)$ with $h_{\mu}(T)<\infty$, where $X$ is a compact metric space, $\mathcal{X}$ is the Borel $\sigma$-algebra on $X$, $\mu$ is a $T$-invariant Borel probability measure and $T$ is a homeomorphism acting on $X$ we show that, if $h_{\mu}(T)>0$, then $h_{\widetilde{\mu}}(\widetilde{T})>0$ for every quasifactor $\widetilde{\mu}$ of $\mu$ having full-support.