Abstract
In this paper, firstly we give a new condition to prove that classical topological entropy is equal to Pesin topological entropy in i.i.d. case. After that, we generalize the concepts of topological entropy of free semigroup actions and study the relationship between the entropies of i.i.d. case and the entropies of free semigroup actions. Finally, for any non-empty subset A⊆Σm+, we introduce the concepts of entropies of any subset A actions and give an analogue of Befutov's formula (the Theorem 1 in [6]) under any subset A actions, which is a supplement of [7].
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