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\(m\)-equivalence, entropy and \(F\)-dynamical systems. (English) Zbl 0982.37006
Summary: The present paper deals with the theory of entropy of \(F\)-dynamical systems using the concept of atoms in a fuzzy \(\sigma\)-algebra. Having introduced the notions of \(m\)-equivalence and \(m\)-refinement, it is proved that entropy of an \(F\)-dynamical system with respect to each \(m\)-equivalence class is an \(m\)-isomorphism invariant. Results proved in this paper include the corresponding classical results as particular cases.

MSC:
37B99 Topological dynamics
28D20 Entropy and other invariants
28D05 Measure-preserving transformations
37A99 Ergodic theory
28E10 Fuzzy measure theory
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