摘要
设T是紧度量空间X上的一个连续变换,μ,υ∈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,υ对任意的不变集B∈B(X)有μ(B)=υ(B)那么μ=υ.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.
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.
出处
《安阳师范学院学报》
2013年第5期19-21,共3页
Journal of Anyang Normal University
关键词
概率测度
不变测度
连续变换
遍历
LEBESGUE积分
Probability measure
Invariant measure
Continuous transformation
Ergodic
Lebesgue integral
