on induced average entropy of random dynamical systems

In this paper, we consider random dynamical systems as a family of continuous maps on a compact metric space, parameterized by a measure space via a noise map. we define a new type of induced entropy for such families, called induced average entropy and will establish the connection between this new quantity and the induced upper capacity topological entropy of its skew product and the topological entropy of the noise map. this relation resembles the abramov-rokhlin theorem in the topological setting.