Entropy characteristics of random transformations

  • Yuri Kifer
Part of the Progress in Probability and Statistics book series (PRPR, volume 10)


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].


Invariant Measure Open Cover Measurable Subset Topological Entropy Conditional Entropy 
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Copyright information

© Birkhäuser Boston, Inc. 1986

Authors and Affiliations

  • Yuri Kifer
    • 1
  1. 1.Institute of Mathematics and Computer ScienceJerusalemIsrael

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