| 关于连续变换的遍历性质的一些注记 |
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| 引用本文： | 郭新伟,鲍晓云.关于连续变换的遍历性质的一些注记[J].应用泛函分析学报,2010,12(4):370-375. |
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| 作者姓名： | 郭新伟 鲍晓云 |
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| 作者单位： | [1]山东大学威海分校数学与统计学院,威海264209 [2]九江学院理学院,九江332005 |
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| 摘 要： | 设(X,d)是一个紧的距离空间,T是(X,d)上的连续变换.利用平均遍历定理证明了:对任意的x∈X,1/n sum from i=0 to n-1 f(T~i x)在C(X)上收敛.该结果是连续变换的Birkhoff型个别遍历定理的推广.由此结果研究了T的其它遍历性质,特别,不依赖深刻的Choquet积分表示定理,给出了遍历分解定理的一个较为简单而直接的证明.
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| 关 键 词： | 连续变换 不变概率测度 遍历性 |
Some Notes on Ergodic Properties for Continuous Transformations |
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| GUO Xinwei,BAO Xiaoyun.Some Notes on Ergodic Properties for Continuous Transformations[J].Acta Analysis Functionalis Applicata,2010,12(4):370-375. |
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| Authors: | GUO Xinwei BAO Xiaoyun |
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| Institution: | 1. School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, China 2. School of Science, Jiujiang College, Jiujiang 332005, China) |
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| Abstract: | Let （X, d） be an compact metric space, T an continuous transformation on （X, d）. It is proved that n/1 n-1∑i=0 f（Tix） converge for any x∈ X using mean ergodic theorem. This result is a strengthening of Birkhoff individual ergodic theorem for continuous transformations. In addition, other ergodic properties of T is also discussed; especially a simple and direct proof of ergodic decomposition for T is given. This proof do not rely on profound Choquet＇s representing theorem. |
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| Keywords: | continuous transformations invariant probability measure ergodicity |
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