| Description |
1 online resource (xxi, 257 pages) : illustrations |
| Series |
Encyclopedia of mathematics and its applications ; v. 12. Section, Real variables |
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Encyclopedia of mathematics and its applications ; v. 12.
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Encyclopedia of mathematics and its applications. Section, Real variables.
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| Contents |
Cover; Half Title; Series Page; Title; Copyright; Dedication; CONTENTS; Editor's Statement; Foreword; Preface; Special Symbols; CHAPTER 1 Topics from Probability Theory; 1.1 Probability Spaces; 1.2 Measurable Partitions and Lebesgue Spaces; 1.3 The Lattice of Measurable Partitions; 1.4 Random Variables; 1.5 Conditional Probability and Independence; 1.6 Conditional Expectation of Random Variables; 1.7 Stochastic Processes and Dynamical Systems; 1.8 The Ergodic Theorem and the Martingale Convergence Theorem; CHAPTER 2 Entropy and Information; 2.1 Information and Uncertainty of Events |
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2.2 The Information Function of an Experiment and Entropy2.3 An Example; 2.4 Conditional Information and Conditional Entropy; 2.5 Properties of Entropy and Conditional Entropy; 2.6 Entropy of Arbitrary Measurable Partitions and Limit Theorems; 2.7 Rate of Information Generation; 2.8 Entropy of Dynamical Systems; 2.9 Factor Automorphisms and Factor Systems; 2.10 Shannon's Theorem and the Equipartition Property; 2.11 Entropy as a Function of Distributions; 2.12 Examples; 2.12.1 Direct Products; 2.12.2 Skew Products; 2.12.3 Powers of Endomorphisms; 2.12 A Flows; 2.12.5 Induced Automorphisms |
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2.12.6 Periodic Automorphisms2.12.7 Rotations of the Circle; 2.12.8 Ergodic Automorphisms of Compact Abelian Groups; 2.12.9 Bernoulli Shifts; 2.12.10 Markov Shifts; 2.12.11 S-Automorphisms; 2.12.12 Unilateral Shifts; 2.12.13 Continued Fraction Transformations; 2.12.14 f-Transformations; 2.13 Sequence Entropy and r-Entropy; CHAPTER 3 Information Theory; 3.1 A Model of an Information System; 3.2 The Source; 3.3 Coding; 3.4 The Channel; 3.5 The Noisy Channel Coding Theorem; 3.6 Source Coding; CHAPTER 4 Ergodic Theory; 4.1 Introduction; 4.2 Unitary Operator of a System and Bernoulli Shifts |
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4.3 K-Systems and K-Automorphisms4.4 Spaces of Ordered Partitions, Weak Independence, and Weak Dependence; 4.5 Coding and Ornstein's Fundamental Lemma; 4.6 The Isomorphism Theorem for Bernoulli Systems; 4.7 Characterization of Bernoulli Systems; 4.8 Relative Isomorphism; 4.9 Special Flows and Equivalence Theory; CHAPTER 5 Topological Dynamics; 5.1 Introduction; 5.2 Definition and Basic Properties of Topological Entropy; 5.3 Connection between Topological and Measure Theoretic Entropy; 5.4 An Alternative Definition of Topological Entropy; CHAPTER 6 Statistical Mechanics; 6.1 Introduction |
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6.2 Classical Continuous Systems6.3 Classical Lattice Systems; 6.4 Gibbs States for Lattice Systems; 6.5 Equilibrium States and the Concepts of Entropy and Pressure; BIBLIOGRAPHY; Index |
| Bibliography |
Includes bibliographical references (pages 245-251) and index |
| Notes |
Print version record |
| Subject |
Entropy (Information theory)
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Ergodic theory.
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Statistical mechanics.
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Topological dynamics.
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MATHEMATICS -- Applied.
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MATHEMATICS -- Probability & Statistics -- General.
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Entropy (Information theory)
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Ergodic theory
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Statistical mechanics
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Topological dynamics
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Entropie
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Theorie
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Mathematik
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| Form |
Electronic book
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| Author |
England, James W.
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| ISBN |
9781461938187 |
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146193818X |
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9781107340718 |
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1107340713 |
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9781107387201 |
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1107387205 |
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