
On Measures of Information and Their Characterizations
Description
Alles über E-Books | Antworten auf Fragen rund um E-Books, Kopierschutz und Dateiformate finden Sie in unserem Info- & Hilfebereich.
More details
Other editions
Additional editions
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
System requirements
File format: PDF
Copy protection: Watermark-DRM (Digital Rights Management)
System requirements:
- Computer (Windows; MacOS X; Linux): Use the free software Adobe Reader, Adobe Digital Editions, or any other PDF viewer of your choice (see eBook Help).
- Tablet/Smartphone (Android; iOS): Install the free app Adobe Digital Editions or another reading app for eBooks, e.g., PocketBook (see eBook Help).
- E-reader: Bookeen, Kobo, Pocketbook, Sony, Tolino and many more (only limited: Kindle).
The file format PDF always displays a book page identically on any hardware. This makes PDF suitable for complex layouts such as those used in textbooks and reference books (images, tables, columns, footnotes). Unfortunately, on the small screens of e-readers or smartphones, PDFs are rather annoying, requiring too much scrolling.
This eBook uses Watermark-DRM, a „soft” copy protection. This means that there are no technical restrictions to prevent illegal distribution. However, there is a personalised watermark embedded in the eBook that can be used to identify the purchaser of the eBook in the event of misuse and to provide evidence for legal purposes.
For more information, see our eBook Help page.