Abstract Methods in Information Theory

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.

Product details

• Authors: Yuichiro Kakihara, Yuichiro (California State Univ Kakihara
• Publisher: World Scientific Publishing Company
• Languages: English
• Product format: Hardback
• Released: 18.10.1999
• EAN: 9789810237110
• ISBN: 978-981-02-3711-0
• No. of pages: 264
• Dimensions: 162 mm x 221 mm x 20 mm
• Weight: 499 g
• Series: Series On Multivariate Analysis; Multivariate Analysis
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics