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Sufficient families and entropy of inverse limit. (English) Zbl 0956.37005
Summary: The purpose of the present paper is to study the metric entropy \(h(\phi , \mathcal N)\) of an \(F\)-measure preserving transformation \(\phi \) relative to a \(\sigma \)-algebra \(\mathcal N\) of an \(F\)-dynamical system. Concepts of sufficient families and generators are introduced and a few results are proved. Finally, the entropy of the inverse limit of an inverse spectrum of \(F\)-dynamical systems is obtained.

MSC:
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37A50 Dynamical systems and their relations with probability theory and stochastic processes
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