| 连续变换下不变测度的性质 |
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| 引用本文： | 常瑾瑾,闫胜业. 连续变换下不变测度的性质[J]. 安阳师范学院学报, 2013, 0(5): 19-21 |
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| 作者姓名： | 常瑾瑾 闫胜业 |
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| 作者单位： | [1]南京信息工程大学滨江学院,江苏南京210044 [2]南京信息工程大学信息与控制学院,江苏南京210044 |
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| 摘 要： | 设T是紧度量空间X上的一个连续变换,μ,v ∈M（X,T）是两个关于T不变的概率测度,利用Birkhoff遍历定理证明：如果μ,v对任意的不变集B∈（96）（X）有μ（B）=v（B）那么μ=v.此结论是不变测度的遍历性质的一个加强,并由此给出了不变测度其它遍历性质较为简单的证明.
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| 关 键 词： | 概率测度 不变测度 连续变换 遍历 Lebesgue积分 |
A Property of Invariant Measure for Continuous Transformation |
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| Affiliation: | CHANG Jin - jin, YAN Sheng - ye( 1. Binjiang School, Nanjing University of Information Science and Technology, Nanjing 210044, China ; 2. Department of Automation, Institute of Information and Control, Nanjing University of Information Science and Technology, Nanjing 210044, China) |
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| Abstract: | Let T be a continuous transformation on a compact metric space X, μ and v [ in μ, v ∈ M （ X, T） ] are two invariant probability measures for T. Using Birkhoff ergodic theorem, a conclusion could be drown that if μ（B） = v（B） for any invariant set B ∈R（ X）, then μ and v are equal ,which is a strengthening of the erg-odic property of invariant measures. Meanwhile, a simple proof of other property about invariant measures is provided. |
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| Keywords: | Probability measure Invariant measure Continuous transformation Ergodic Lebesgue integral |
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