Uniform and Semi-uniform Convergence for Discontinuous Skew-product Transformation and Observation

In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation and observation function are ignorable in some measure-theoretical sense. The theorems extend the classical results which have been established for continuous transformations and continuous observation functions.