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The Entropy Ergodic Theorem

  • Robert M. Gray
Chapter

Abstract

The goal of this chapter is to prove an ergodic theorem for sample entropy of finite-alphabet random processes. The result is sometimes called the ergodic theorem of information theory or the asymptotic equipartition (AEP) theorem, but it is best known as the Shannon-McMillan-Breiman theorem. It provides a common foundation to many of the results of both ergodic theory and information theory.

Keywords

Ergodic Theorem Invariant Function Sample Entropy Entropy Rate Martingale Theory 
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Copyright information

© Springer Science + Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Electrical EngineeringStanford UniversityStanfordUSA

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