RELATIVE MODEL OF THE LOGICAL ENTROPY OF SUB-σΘ-ALGEBRAS

In the context of observers, any mathematical model accord-ing to the viewpoint of an observer Θ is called a relative model. The purpose of the present paper is to study the relative model of logical en-tropy. Given an observer Θ, we define the relative logical entropy and relative conditional logical entropy of a sub-σΘ-algebra having finitely many atoms on the relative probability Θ−measure space and prove the ergodic properties of these measures. Finally, it is shown that the relative logical entropy is invariant under the relation of equivalence modulo zero.