Abstract
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 [32] 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 [36], Peterson [39] and Walters [46].
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© 1986 Birkhäuser Boston, Inc.
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Kifer, Y. (1986). Entropy characteristics of random transformations. In: Ergodic Theory of Random Transformations. Progress in Probability and Statistics, vol 10. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-9175-3_3
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DOI: https://doi.org/10.1007/978-1-4684-9175-3_3
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4684-9177-7
Online ISBN: 978-1-4684-9175-3
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