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.

中文翻译：

---

不连续斜积变换和观测的均匀和半均匀收敛

对于具有可积分观测函数的不连续偏积变换，本文获得了均匀的遍历定理和半均匀的遍历定理。主要假设是，变换和观测函数的不连续集在某种度量理论意义上是可忽略的。该定理扩展了为连续变换和连续观测函数建立的经典结果。