On Measures of Information and Their Characterizations
Published on 14. May 2014
247 pages
978-0-08-095624-4 (ISBN)
Description
This book deals with measures of information (the most important ones being called entropies), their properties, and, reciprocally, with questions concerning which of these properties determine known measures of information, and which are the most general formulas satisfying reasonable requirements on practical measures of information. Thisis the first book investigating this subject in depth.
More details
Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095624-4 (9780080956244)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
J. Aczel | Zoltan Daroczy
On Measures of Information and Their Characterizations
Book
01/1975
Academic Press
€86.19
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Content
- 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 Coding
- 1.5 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 Probabilities
- 3.3 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 Entropies
- 5.3 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 Distributions
- References
- Author Index
- Subject Index
