Description

Book Synopsis
The isomorphism problem of ergodic theory has been extensively studied since Kolmogorov's introduction of entropy into the subject and especially since Ornstein's solution for Bernoulli processes. Much of this research has been in the abstract measure-theoretic setting of pure ergodic theory. However, there has been growing interest in isomorphisms of a more restrictive and perhaps more realistic nature which recognize and respect the state structure of processes in various ways. These notes give an account of some recent developments in this direction. A special feature is the frequent use of the information function as an invariant in a variety of special isomorphism problems. Lecturers and postgraduates in mathematics and research workers in communication engineering will find this book of use and interest.

Table of Contents
1. Introduction; 2. The Information Cocycle; 3. Finitary Isomorphisms; 4. Block-codes; 5. Classifications of Topological Markov Chains.

LMS 67 Classification Problems London Mathematical Society Lecture Note Series Series Number 67

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      View other formats and editions of LMS 67 Classification Problems London Mathematical Society Lecture Note Series Series Number 67 by William Parry

      Publisher: Cambridge University Press
      Publication Date: 7/8/1982 12:00:00 AM
      ISBN13: 9780521287944, 978-0521287944
      ISBN10: 0521287944
      Also in:
      Probability and statistics

      Description

      Book Synopsis
      The isomorphism problem of ergodic theory has been extensively studied since Kolmogorov's introduction of entropy into the subject and especially since Ornstein's solution for Bernoulli processes. Much of this research has been in the abstract measure-theoretic setting of pure ergodic theory. However, there has been growing interest in isomorphisms of a more restrictive and perhaps more realistic nature which recognize and respect the state structure of processes in various ways. These notes give an account of some recent developments in this direction. A special feature is the frequent use of the information function as an invariant in a variety of special isomorphism problems. Lecturers and postgraduates in mathematics and research workers in communication engineering will find this book of use and interest.

      Table of Contents
      1. Introduction; 2. The Information Cocycle; 3. Finitary Isomorphisms; 4. Block-codes; 5. Classifications of Topological Markov Chains.

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