## Characterizations of Information Measures"This book is highly recommended for all those whose interests lie in the fields that deal with any kind of information measures. It will also find readers in the field of functional analysis..".Mathematical Reviews |

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### Contents

Introduction Preliminaries and Notation | 1 |

The Branching Property | 29 |

Recursivity Properties | 51 |

The Fundamental Equation of Information | 81 |

Sum Form Information Measures | 107 |

Basic Sum Form Functional Equations | 117 |

### Common terms and phrases

1-dimensional abelian group Aczel additive function an-i apply Theorem arbitrary arrive assume branching property Cauchy functional equations Chapter characteristic functional characterization cocycle coefficients completes the proof constant contradiction Daroczy defined entropies of degree equation of information exists extension F satisfies F(pq fixed form information measures function F functional equation fundamental equation given h(pq Hence i=l j=l implies In(P induction information theory integers Jarai Lebesgue measurable Lemma Let F linear linearly independent log(l logarithmic logp M(pi m)-additive Math measurable functions measurable solutions measures of information Moreover multiplicative functions multiplicative type nonconstant nonempty notation numbers obtain open domain open set polynomial positive cone projection proof of Theorem prove recursive of type Remark representation respectively satisfy the functional semigroup Shannon entropy solution of 5.2.2 solve subring Substituting sum form information suppose symmetric theory tion variable vector Verification of Step yields zero