Entropy characteristics of random transformations
The concept of entropy has played a major part in ergodic theory so far. In this chapter we introduce the notions of both measure theoretic (metric) and topological entropies for compositions of random maps. These entropies turn out to be the “mixed” or “relative” entropies of Abramov-Rohlin [l] and Ledrappier-Walters  corresponding to the skew product transformation τ but our motivation and the set up are different from theirs. We shall review facts from the deterministic theory of entropy. More comprehensive expositions can be found in Martin and England , Peterson  and Walters .
KeywordsInvariant Measure Open Cover Measurable Subset Topological Entropy Conditional Entropy
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