## Entropy and ergodic theory |

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### Contents

GENERALIZED GAMMAENTROPY | 15 |

AN ALTERNATIVE CHARACTERIZATION OF INFOR | 39 |

ON RENYISHANNON ENTROPY AND RELATED | 65 |

Copyright | |

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### Common terms and phrases

Aczel admits a cyclic admits a nonmeasure-preserving admits a uniform approximation with speed atoms automorphism T admits Canada Professor coarse graining Corollary cyclic approximation defined Definition denote differentiable directed divergence dyadic transformation dynamical system elements equivalence ERGODIC THEORY example finite set finite sub-a-field ft(l Gibbs given Ha(P Hartley entropies Hence HX(P Hy R0 information divergence Information Theory initial condition initial measure invariant measure Ising model Kannappan Katok and Stepin Lebesgue measure log w(P log2 Markov chain Markov random field Markov system Math measure-preserving monotonic nearest neighbour nonmeasure-preserving approximation obtain partition postulates probability distribution probability measure problem proof proved pu p2 random variable Renyi's entropy result reversible satisfy Shannon's entropy Shannon's inequality statistical mechanics stochastic system subsets symmetric synchronous cellular system Theorem tion tonian uniform approximation University y-entropy