On Measures of Information and Their Characterizations

Name: On Measures of Information and Their Characterizations
Brand: Academic Press
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ACZEL(Autor*in)

Acze?l(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

247 Seiten

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Inhalt

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

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