Abstract Methods In Information Theory; Author: Kakihara, Yuichiro; Hardback; Book

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Abstract Methods In Information Theory

Author: Kakihara, Yuichiro
Series#:4; Series on Multivariate Analysis; Hardback; Book
264 pages
Published: November 1999
World Scientific Publishing Co Pte Ltd
ISBN: 9810237111

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 consideThe main purpose of this text is to present information channels in the environment of real and functional analysis as well as probability theory. Further aspects of information channels including measurability, approximation and noncommuntative extensions are also discussed.

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