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| Considering a concave function $g\colon [0,1]\mapsto \mathbb{R}$ vanishing at the origin instead of the Shannon entropy function $\eta(x)=-x\ln x$, $\eta(0):=0$, leads to the generalizations of dynamical and measure-theoretic entropies . We will show the connections of these generalizations with the dynamical and Kolmogorov-Sinai entropies. We will also introduce the concept of types of $g$-entropy convergence rates introduced by Blume \cite{Blume97} and discuss some results concerning this quantity.
\bibitem{Blume97} F. Blume. Possible rates of entropy convergence \emph{Ergodic Theory \& Dynam. Systems} (1997), {\bf 17}, 45-70. |
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