On measures of information and their characterizations /:
On measures of information and their characterizations.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Academic Press,
1975.
|
| Schriftenreihe: | Mathematics in science and engineering ;
v. 115. |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Zusammenfassung: | On measures of information and their characterizations. |
| Beschreibung: | 1 online resource (xii, 234 pages) |
| Bibliographie: | Includes bibliographical references (pages 219-226) and indexes. |
| ISBN: | 9780120437603 0120437600 9780080956244 0080956246 |
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| 490 | 1 | |a Mathematics in science and engineering ; |v v. 115 | |
| 504 | |a Includes bibliographical references (pages 219-226) and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Front Cover; On Measures of Information and Their Characterizations; Copyright Page; Contents; Preface; Chapter 0. Introduction. Entropy of a Single Event. Functional Equations; 0.1 Introduction, History; 0.2 Entropy of One Event; 0.3 The Cauchy Functional Equation and Related Equations; 0.4 Completely Additive Number Theoretical Functions; Chapter 1. Shannon's Measure of Information; 1.1 Shannon's Entropy; 1.2 Algebraic Properties of the Shannon Entropy; 1.3 Analytic Properties of the Shannon Entropy. Inequalities | |
| 505 | 8 | |a 1.4 Some Simple Examples of Applications of Entropies to Logical Games and Coding1.5 Coding; 1.6 Optimal Coding and Entropy; Chapter 2. Some Desirable Properties of Entropies and Their Correlations. The Hincin and Faddeev Characterizations of Shannon's Entropy; 2.1 A List of Desiderata for Entropies; 2.2 Generalized Representations; 2.3 Correlations and Simple Consequences of the Desiderata; 2.4 The Shannon-Hincin and the Faddeev Characterizations of the Shannon Entropy; Chapter 3. The Fundamental Equation of Information; 3.1 Information Functions | |
| 505 | 8 | |a 3.2 Information Functions Continuous at the Origin-Entropies Which Are Small for Small Probabilities3.3 Nonnegative Bounded Information Functions and Entropies; 3.4 Measurable Information Functions and Entropies; 3.5 The General Solution of the Fundamental Equation of Information; Chapter 4. Further Characterizations of tbe Shannon Entropy; 4.1 The Branching Property; 4.2 Entropies with the Sum Property; 4.3 Characterization of the Shannon Entropy by the Shannon Inequality; 4.4 Subadditive Additive Entropies; Chapter 5. Rényi Entropies; 5.1 Entropies and Mean Values | |
| 505 | 8 | |a 5.2 Equality of Average Probabilities. Additivity of Average Entropies5.3 Rényi Entropies for Possibly Incomplete Distributions; 5.4 Optimal Coding and Rényi Entropies; 5.5 Characterization of ß-Averages; Chapter 6. Generalized Information Functions; 6.1 Relative Information; 6.2 Information Functions of Degree a; 6.3 Generalized Entropies; Chapter 7. Further Measures of Information; 7.1 Further Entropies. Other Measures of Information Derived Algebraically from Entropies; 7.2 Further Measures of Information Depending on Two Probability Distributions | |
| 505 | 8 | |a 7.3 Some Measures of Information Depending on Three DistributionsReferences; Author Index; Subject Index | |
| 520 | |a On measures of information and their characterizations. | ||
| 650 | 0 | |a Entropy (Information theory) |0 http://id.loc.gov/authorities/subjects/sh85044152 | |
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| contents | Front Cover; On Measures of Information and Their Characterizations; Copyright Page; Contents; Preface; Chapter 0. Introduction. Entropy of a Single Event. Functional Equations; 0.1 Introduction, History; 0.2 Entropy of One Event; 0.3 The Cauchy Functional Equation and Related Equations; 0.4 Completely Additive Number Theoretical Functions; Chapter 1. Shannon's Measure of Information; 1.1 Shannon's Entropy; 1.2 Algebraic Properties of the Shannon Entropy; 1.3 Analytic Properties of the Shannon Entropy. Inequalities 1.4 Some Simple Examples of Applications of Entropies to Logical Games and Coding1.5 Coding; 1.6 Optimal Coding and Entropy; Chapter 2. Some Desirable Properties of Entropies and Their Correlations. The Hincin and Faddeev Characterizations of Shannon's Entropy; 2.1 A List of Desiderata for Entropies; 2.2 Generalized Representations; 2.3 Correlations and Simple Consequences of the Desiderata; 2.4 The Shannon-Hincin and the Faddeev Characterizations of the Shannon Entropy; Chapter 3. The Fundamental Equation of Information; 3.1 Information Functions 3.2 Information Functions Continuous at the Origin-Entropies Which Are Small for Small Probabilities3.3 Nonnegative Bounded Information Functions and Entropies; 3.4 Measurable Information Functions and Entropies; 3.5 The General Solution of the Fundamental Equation of Information; Chapter 4. Further Characterizations of tbe Shannon Entropy; 4.1 The Branching Property; 4.2 Entropies with the Sum Property; 4.3 Characterization of the Shannon Entropy by the Shannon Inequality; 4.4 Subadditive Additive Entropies; Chapter 5. Rényi Entropies; 5.1 Entropies and Mean Values 5.2 Equality of Average Probabilities. Additivity of Average Entropies5.3 Rényi Entropies for Possibly Incomplete Distributions; 5.4 Optimal Coding and Rényi Entropies; 5.5 Characterization of ß-Averages; Chapter 6. Generalized Information Functions; 6.1 Relative Information; 6.2 Information Functions of Degree a; 6.3 Generalized Entropies; Chapter 7. Further Measures of Information; 7.1 Further Entropies. Other Measures of Information Derived Algebraically from Entropies; 7.2 Further Measures of Information Depending on Two Probability Distributions 7.3 Some Measures of Information Depending on Three DistributionsReferences; Author Index; Subject Index |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:42Z |
| institution | BVB |
| isbn | 9780120437603 0120437600 9780080956244 0080956246 |
| language | English |
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| series2 | Mathematics in science and engineering ; |
| spelling | Aczél, J. http://id.loc.gov/authorities/names/n50037016 On measures of information and their characterizations / J. Aczél, Z. Daróczy. New York : Academic Press, 1975. 1 online resource (xii, 234 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics in science and engineering ; v. 115 Includes bibliographical references (pages 219-226) and indexes. Print version record. Front Cover; On Measures of Information and Their Characterizations; Copyright Page; Contents; Preface; Chapter 0. Introduction. Entropy of a Single Event. Functional Equations; 0.1 Introduction, History; 0.2 Entropy of One Event; 0.3 The Cauchy Functional Equation and Related Equations; 0.4 Completely Additive Number Theoretical Functions; Chapter 1. Shannon's Measure of Information; 1.1 Shannon's Entropy; 1.2 Algebraic Properties of the Shannon Entropy; 1.3 Analytic Properties of the Shannon Entropy. Inequalities 1.4 Some Simple Examples of Applications of Entropies to Logical Games and Coding1.5 Coding; 1.6 Optimal Coding and Entropy; Chapter 2. Some Desirable Properties of Entropies and Their Correlations. The Hincin and Faddeev Characterizations of Shannon's Entropy; 2.1 A List of Desiderata for Entropies; 2.2 Generalized Representations; 2.3 Correlations and Simple Consequences of the Desiderata; 2.4 The Shannon-Hincin and the Faddeev Characterizations of the Shannon Entropy; Chapter 3. The Fundamental Equation of Information; 3.1 Information Functions 3.2 Information Functions Continuous at the Origin-Entropies Which Are Small for Small Probabilities3.3 Nonnegative Bounded Information Functions and Entropies; 3.4 Measurable Information Functions and Entropies; 3.5 The General Solution of the Fundamental Equation of Information; Chapter 4. Further Characterizations of tbe Shannon Entropy; 4.1 The Branching Property; 4.2 Entropies with the Sum Property; 4.3 Characterization of the Shannon Entropy by the Shannon Inequality; 4.4 Subadditive Additive Entropies; Chapter 5. Rényi Entropies; 5.1 Entropies and Mean Values 5.2 Equality of Average Probabilities. Additivity of Average Entropies5.3 Rényi Entropies for Possibly Incomplete Distributions; 5.4 Optimal Coding and Rényi Entropies; 5.5 Characterization of ß-Averages; Chapter 6. Generalized Information Functions; 6.1 Relative Information; 6.2 Information Functions of Degree a; 6.3 Generalized Entropies; Chapter 7. Further Measures of Information; 7.1 Further Entropies. Other Measures of Information Derived Algebraically from Entropies; 7.2 Further Measures of Information Depending on Two Probability Distributions 7.3 Some Measures of Information Depending on Three DistributionsReferences; Author Index; Subject Index On measures of information and their characterizations. Entropy (Information theory) http://id.loc.gov/authorities/subjects/sh85044152 Entropie (Théorie de l'information) REFERENCE Questions & Answers. bisacsh Entropy (Information theory) fast Daróczy, Zoltán. http://id.loc.gov/authorities/names/nb2002025295 Print version: Aczél, J. On measures of information and their characterizations. New York : Academic Press, 1975 9780120437603 (DLC) 74017968 (OCoLC)1175852 Mathematics in science and engineering ; v. 115. http://id.loc.gov/authorities/names/n42015986 FWS01 ZDB-4-EBA FWS_PDA_EBA https://www.sciencedirect.com/science/bookseries/00765392/115 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=296977 Volltext |
| spellingShingle | Aczél, J. On measures of information and their characterizations / Mathematics in science and engineering ; Front Cover; On Measures of Information and Their Characterizations; Copyright Page; Contents; Preface; Chapter 0. Introduction. Entropy of a Single Event. Functional Equations; 0.1 Introduction, History; 0.2 Entropy of One Event; 0.3 The Cauchy Functional Equation and Related Equations; 0.4 Completely Additive Number Theoretical Functions; Chapter 1. Shannon's Measure of Information; 1.1 Shannon's Entropy; 1.2 Algebraic Properties of the Shannon Entropy; 1.3 Analytic Properties of the Shannon Entropy. Inequalities 1.4 Some Simple Examples of Applications of Entropies to Logical Games and Coding1.5 Coding; 1.6 Optimal Coding and Entropy; Chapter 2. Some Desirable Properties of Entropies and Their Correlations. The Hincin and Faddeev Characterizations of Shannon's Entropy; 2.1 A List of Desiderata for Entropies; 2.2 Generalized Representations; 2.3 Correlations and Simple Consequences of the Desiderata; 2.4 The Shannon-Hincin and the Faddeev Characterizations of the Shannon Entropy; Chapter 3. The Fundamental Equation of Information; 3.1 Information Functions 3.2 Information Functions Continuous at the Origin-Entropies Which Are Small for Small Probabilities3.3 Nonnegative Bounded Information Functions and Entropies; 3.4 Measurable Information Functions and Entropies; 3.5 The General Solution of the Fundamental Equation of Information; Chapter 4. Further Characterizations of tbe Shannon Entropy; 4.1 The Branching Property; 4.2 Entropies with the Sum Property; 4.3 Characterization of the Shannon Entropy by the Shannon Inequality; 4.4 Subadditive Additive Entropies; Chapter 5. Rényi Entropies; 5.1 Entropies and Mean Values 5.2 Equality of Average Probabilities. Additivity of Average Entropies5.3 Rényi Entropies for Possibly Incomplete Distributions; 5.4 Optimal Coding and Rényi Entropies; 5.5 Characterization of ß-Averages; Chapter 6. Generalized Information Functions; 6.1 Relative Information; 6.2 Information Functions of Degree a; 6.3 Generalized Entropies; Chapter 7. Further Measures of Information; 7.1 Further Entropies. Other Measures of Information Derived Algebraically from Entropies; 7.2 Further Measures of Information Depending on Two Probability Distributions 7.3 Some Measures of Information Depending on Three DistributionsReferences; Author Index; Subject Index Entropy (Information theory) http://id.loc.gov/authorities/subjects/sh85044152 Entropie (Théorie de l'information) REFERENCE Questions & Answers. bisacsh Entropy (Information theory) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85044152 |
| title | On measures of information and their characterizations / |
| title_auth | On measures of information and their characterizations / |
| title_exact_search | On measures of information and their characterizations / |
| title_full | On measures of information and their characterizations / J. Aczél, Z. Daróczy. |
| title_fullStr | On measures of information and their characterizations / J. Aczél, Z. Daróczy. |
| title_full_unstemmed | On measures of information and their characterizations / J. Aczél, Z. Daróczy. |
| title_short | On measures of information and their characterizations / |
| title_sort | on measures of information and their characterizations |
| topic | Entropy (Information theory) http://id.loc.gov/authorities/subjects/sh85044152 Entropie (Théorie de l'information) REFERENCE Questions & Answers. bisacsh Entropy (Information theory) fast |
| topic_facet | Entropy (Information theory) Entropie (Théorie de l'information) REFERENCE Questions & Answers. |
| url | https://www.sciencedirect.com/science/bookseries/00765392/115 https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=296977 |
| work_keys_str_mv | AT aczelj onmeasuresofinformationandtheircharacterizations AT daroczyzoltan onmeasuresofinformationandtheircharacterizations |