The Observational Modelling of Information Function with Finite Partitions

In this paper we study the notions of relative information function and relative conditional information function on a relative probability measure space. We present some examples and prove some theorems about them. Also the concept of relative information function for a relative measure preserving transformation is introduced and some of its properties, are proved. Finally, it is proved that the relative information function of relative measure preserving transformations is invariant under isomorphism.