Characterization Of Information MeasuresHow should information be measured? That is the motivating question for this book. The concept of information has become so pervasive that people regularly refer to the present era as the Information Age. Information takes many forms: oral, written, visual, electronic, mechanical, electromagnetic, etc. Many recent inventions deal with the storage, transmission, and retrieval of information. From a mathematical point of view, the most basic problem for the field of information theory is how to measure information. In this book we consider the question: What are the most desirable properties for a measure of information to possess? These properties are then used to determine explicitly the most “natural” (i.e. the most useful and appropriate) forms for measures of information.This important and timely book presents a theory which is now essentially complete. The first book of its kind since 1975, it will bring the reader up to the current state of knowledge in this field. |
Contents
| 1 | |
CHAPTER 2 THE BRANCHING PROPERTY | 29 |
CHAPTER 3 RECURSIVITY PROPERTIES | 51 |
CHAPTER 4 THE FUNDAMENTAL EQUATION OF INFORMATION AND REGULAR RECURSIVE MEASURES | 81 |
CHAPTER 5 SUM FORM INFORMATION MEASURES AND ADDITIVITY PROPERTIES | 107 |
CHAPTER 6 BASIC SUM FORM FUNCTIONAL EQUATIONS | 117 |
Common terms and phrases
1-dimensional 3-symmetric a₁ abelian group Aczél additive function arbitrary arrive assume B.R. Ebanks branching property Cauchy functional equations Chapter completes the proof constant d₁ D₂ defined entropies of degree equation of information exists F satisfies F(pi F(pq form information measures function F functional equation fundamental equation ƒ pq given Hence implies In(P information theory integers JR satisfy Kannappan Lebesgue measurable Lemma Let f linear linearly independent logarithmic M₁ M₁(p M₂ M₂(p Math measurable functions measurable solutions measures of information Moreover multiplicative functions multiplicative type nonconstant numbers obtain open domain open set P₁ polynomial positive cone projection prove recursive Remark representation respectively result Sahoo Sander Shannon entropy solution of 5.2.2 Substituting sum form information suppose symmetric theory tion vector Verification of Step yields zero ΣΣ РЕЈ