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5 - Infinite Invariant Measures: Finer Properties

from Part I - Ergodic Theory and Geometric Measures

Published online by Cambridge University Press:  20 April 2023

Janina Kotus  and
Mariusz Urbański
Janina Kotus
Affiliation:
Warsaw University of Technology
Mariusz Urbański
Affiliation:
University of North Texas
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Summary

In this chapter, we provide a classical account of Kolmogorov–Sinai metric entropy for measure-preserving dynamical systems. We prove the Shannon–McMillan–Breimann Theorem and, based on Abramov's Formula, define the concept of Krengel's Entropy of a conservative system preserving a (possibly infinite) invariant measure.

Keywords

Kolmogorov–Sinai entropyShannon–McMillan–Breimann TheoremKrengel's Entropy
Type
Chapter
Information
Meromorphic Dynamics
Abstract Ergodic Theory, Geometry, Graph Directed Markov Systems, and Conformal Measures
 , pp. 134 - 159
Publisher: Cambridge University Press
Print publication year: 2023

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