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Some Problems of Ergodic Theory and Information Theory.
No full textThe subject of ergodic theory which is the mathematical outgrowth of the gas problem in statistical machines and the subject of information theory which in the mathematical outgrowth of the problem of information transmission through communication channels have many interesting dual features. In ergodic theory we study collectively and individually the measure preserving transformations of a first measure space, where as in information theory we do the same with the set of all measured in variant under a fixed measurable transformation of a measurable space. The object of this thesis it to study some of the dual relations between the two theories with emphasis on the informations-theoretic aspect