Classification problems in ergodic theory / William Parry and Selim Tuncel

Auteur: Parry, William (1934-2006) - AuteurCo-auteur: Tuncel, Selim (1957-) - AuteurType de document: MonographieCollection: London Mathematical Society lecture note series ; 67Langue: anglaisPays: Grande BretagneÉditeur: Cambridge : Cambridge University Press, 1982Description: 1 vol. (101 p.) : ill. ; 23 cm ISBN: 0521287944 ; br. Résumé: 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. (source : CUP).Bibliographie: Bibliogr. p. 96-99. Index. Sujets MSC: 28D05 Measure and integration -- Measure-theoretic ergodic theory -- Measure-preserving transformations
28D20 Measure and integration -- Measure-theoretic ergodic theory -- Entropy and other invariants
60G10 Probability theory and stochastic processes -- Stochastic processes -- Stationary processes
54H20 General topology -- Connections with other structures, applications -- Topological dynamics
60J27 Probability theory and stochastic processes -- Markov processes -- Continuous-time Markov processes on discrete state spaces
En-ligne: Zentralblatt | MathSciNet | CUP
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Bibliogr. p. 96-99. Index

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. (source : CUP)

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