Mathematical theory of entropy /:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [Cambridgeshire] ; New York, NY, USA :
Cambridge University Press,
©1984.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 12. Encyclopedia of mathematics and its applications. Section, Real variables. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 1 online resource (xxi, 257 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 245-251) and index. |
| ISBN: | 9781461938187 146193818X 9781107340718 1107340713 9781107387201 1107387205 |
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| 245 | 1 | 0 | |a Mathematical theory of entropy / |c Nathaniel F.G. Martin, James W. England ; foreword by James K. Brooks. |
| 260 | |a Cambridge [Cambridgeshire] ; |a New York, NY, USA : |b Cambridge University Press, |c ©1984. | ||
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| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v v. 12. |a Section, Real variables | |
| 504 | |a Includes bibliographical references (pages 245-251) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 650 | 0 | |a Entropy (Information theory) |0 http://id.loc.gov/authorities/subjects/sh85044152 | |
| 650 | 0 | |a Ergodic theory. |0 http://id.loc.gov/authorities/subjects/sh85044600 | |
| 650 | 0 | |a Statistical mechanics. |0 http://id.loc.gov/authorities/subjects/sh85127571 | |
| 650 | 0 | |a Topological dynamics. |0 http://id.loc.gov/authorities/subjects/sh85136080 | |
| 650 | 6 | |a Entropie (Théorie de l'information) | |
| 650 | 6 | |a Théorie ergodique. | |
| 650 | 6 | |a Mécanique statistique. | |
| 650 | 6 | |a Dynamique topologique. | |
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| author | Martin, Nathaniel F. G. |
| author2 | England, James W. |
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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 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 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 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 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 |
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| discipline | Mathematik |
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| id | ZDB-4-EBA-ocn856021436 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:29Z |
| institution | BVB |
| isbn | 9781461938187 146193818X 9781107340718 1107340713 9781107387201 1107387205 |
| language | English |
| oclc_num | 856021436 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxi, 257 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; Encyclopedia of mathematics and its applications. Section, Real variables. |
| series2 | Encyclopedia of mathematics and its applications ; Section, Real variables |
| spelling | Martin, Nathaniel F. G. http://id.loc.gov/authorities/names/n81010125 Mathematical theory of entropy / Nathaniel F.G. Martin, James W. England ; foreword by James K. Brooks. Cambridge [Cambridgeshire] ; New York, NY, USA : Cambridge University Press, ©1984. 1 online resource (xxi, 257 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; v. 12. Section, Real variables Includes bibliographical references (pages 245-251) and index. Print version record. 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 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 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 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 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 Entropy (Information theory) http://id.loc.gov/authorities/subjects/sh85044152 Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Statistical mechanics. http://id.loc.gov/authorities/subjects/sh85127571 Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Entropie (Théorie de l'information) Théorie ergodique. Mécanique statistique. Dynamique topologique. MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Entropy (Information theory) fast Ergodic theory fast Statistical mechanics fast Topological dynamics fast Entropie gnd http://d-nb.info/gnd/4014894-4 Theorie gnd Mathematik gnd England, James W. http://id.loc.gov/authorities/names/n81010124 Print version: Martin, Nathaniel F.G. Mathematical theory of entropy. Cambridge [Cambridgeshire] ; New York, NY, USA : Cambridge University Press, ©1984 0521302323 (DLC) 85121434 (OCoLC)12081912 Encyclopedia of mathematics and its applications ; v. 12. http://id.loc.gov/authorities/names/n42010632 Encyclopedia of mathematics and its applications. Section, Real variables. http://id.loc.gov/authorities/names/n84711569 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=616937 Volltext |
| spellingShingle | Martin, Nathaniel F. G. Mathematical theory of entropy / Encyclopedia of mathematics and its applications ; Encyclopedia of mathematics and its applications. Section, Real variables. 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 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 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 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 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 Entropy (Information theory) http://id.loc.gov/authorities/subjects/sh85044152 Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Statistical mechanics. http://id.loc.gov/authorities/subjects/sh85127571 Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Entropie (Théorie de l'information) Théorie ergodique. Mécanique statistique. Dynamique topologique. MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Entropy (Information theory) fast Ergodic theory fast Statistical mechanics fast Topological dynamics fast Entropie gnd http://d-nb.info/gnd/4014894-4 Theorie gnd Mathematik gnd |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85044152 http://id.loc.gov/authorities/subjects/sh85044600 http://id.loc.gov/authorities/subjects/sh85127571 http://id.loc.gov/authorities/subjects/sh85136080 http://d-nb.info/gnd/4014894-4 |
| title | Mathematical theory of entropy / |
| title_auth | Mathematical theory of entropy / |
| title_exact_search | Mathematical theory of entropy / |
| title_full | Mathematical theory of entropy / Nathaniel F.G. Martin, James W. England ; foreword by James K. Brooks. |
| title_fullStr | Mathematical theory of entropy / Nathaniel F.G. Martin, James W. England ; foreword by James K. Brooks. |
| title_full_unstemmed | Mathematical theory of entropy / Nathaniel F.G. Martin, James W. England ; foreword by James K. Brooks. |
| title_short | Mathematical theory of entropy / |
| title_sort | mathematical theory of entropy |
| topic | Entropy (Information theory) http://id.loc.gov/authorities/subjects/sh85044152 Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Statistical mechanics. http://id.loc.gov/authorities/subjects/sh85127571 Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Entropie (Théorie de l'information) Théorie ergodique. Mécanique statistique. Dynamique topologique. MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Entropy (Information theory) fast Ergodic theory fast Statistical mechanics fast Topological dynamics fast Entropie gnd http://d-nb.info/gnd/4014894-4 Theorie gnd Mathematik gnd |
| topic_facet | Entropy (Information theory) Ergodic theory. Statistical mechanics. Topological dynamics. Entropie (Théorie de l'information) Théorie ergodique. Mécanique statistique. Dynamique topologique. MATHEMATICS Applied. MATHEMATICS Probability & Statistics General. Ergodic theory Statistical mechanics Topological dynamics Entropie Theorie Mathematik |
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| work_keys_str_mv | AT martinnathanielfg mathematicaltheoryofentropy AT englandjamesw mathematicaltheoryofentropy |