The observational modelling of information function with finite partitions

Abstract

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 properties of it, are proved. At end, it is proved that the rlative information function of relative measure preserving transformations is invariant under isomorphism.