Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran.

Abstract

In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $\Theta$. The relative entropy of a sub-$\sigma_\Theta$-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a relative $\Theta$-measure preserving transformations with respect to a relative sub-$\sigma_\Theta$-algebra having finite atoms is affine.

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