For a homeomorphism $T$ on a compact metric space $X$, a $T$-invariant Borel probability measure $\mu$ on $X$ and a measure-theoretic quasifactor $\widetilde{ \mu}$ of $\mu$, we study the relationship between the local entropy of the system $(X,\mu,T)$ and of its induced system $(\mathcal{ M}(X),\widetilde{ \mu},\widetilde{ T})$, where $\widetilde{ T}$ is the homeomorphism induced by $T$ on the space $\mathcal{ M}(X)$ of all Borel probability measures defined on $X$.
Categories: math.DS
