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

• 作者: Xia PAN Zuo Huan ZHENG Zhe ZHOU
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 333-344
• 页数: 12页
• 语种: 英文

摘要

In this paper, for a discontinuous skew-product transformation with the integrable ob-servation 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.