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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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References:
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