Abstract Methods In Information Theory(English, Hardcover, Kakihara Yuichiro)

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Abstract Methods In Information Theory(English, Hardcover, Kakihara Yuichiro) is written by Kakihara Yuichiro and published by World Scientific Publishing Co Pte Ltd. It's available with International Standard Book Number or ISBN identification 9810237111 (ISBN 10) and 9789810237110 (ISBN 13).

Information Theory is studied from the following view points: (1) the theory of entropy as amount of information; (2) the mathematical structure of information sources (probability measures); and (3) the theory of information channels. Shannon entropy and Kolmogorov-Sinai entropy are defined and their basic properties are examined, where the latter entropy is extended to be a linear functional on a certain set of measures. Ergodic and mixing properties of stationary sources are studied as well as AMS (asymptotically mean stationary) sources. The main purpose of this book is to present information channels in the environment of real and functional analysis as well as probability theory. Ergodic channels are characterized in various manners. Mixing and AMS channels are also considered in detail with some illustrations. A few other aspects of information channels including measurability, approximation and noncommutative extensions, are also discussed.