利用Fubini定理和单调类方法给出乘积距离空间上的概率测度成为乘积测度的一个充分必要条件,即乘积可测空间(multiply from i=1 to n(X_i),multiply from i=1 to n(B(X_i)))的概率测度μ为Borel概率测度的乘积测度的充分必要条件是multi...利用Fubini定理和单调类方法给出乘积距离空间上的概率测度成为乘积测度的一个充分必要条件,即乘积可测空间(multiply from i=1 to n(X_i),multiply from i=1 to n(B(X_i)))的概率测度μ为Borel概率测度的乘积测度的充分必要条件是multiply from i=1 to n(X_i)multiply from i=1 to n(f_id_μ)=multiply from i=1 to n multiply from i=1 to n(X_i)f_id_μ,其中fi(i=1,2,…,n)是Xi上任一有界连续函数.展开更多
In this paper,a necessary and sufficient condition of a measure to be the product Borel probability measure on the product space of some compact metric spaces are given.
In this paper,we introduce the concept of measure-theoretic r-entropy of a continuous map on a compact metric space,and get the results as follows:1.Measure-theoretic entropy is the limit of measure-theoretic r-entrop...In this paper,we introduce the concept of measure-theoretic r-entropy of a continuous map on a compact metric space,and get the results as follows:1.Measure-theoretic entropy is the limit of measure-theoretic r-entropy and topological entropy is the limit of topological r-entropy(r → 0);2.Topological r-entropy is more than or equal to the supremum of 4r-entropy in the sense of Feldman's definition,where the measure varies among all the ergodic Borel probability measures.展开更多
文摘利用Fubini定理和单调类方法给出乘积距离空间上的概率测度成为乘积测度的一个充分必要条件,即乘积可测空间(multiply from i=1 to n(X_i),multiply from i=1 to n(B(X_i)))的概率测度μ为Borel概率测度的乘积测度的充分必要条件是multiply from i=1 to n(X_i)multiply from i=1 to n(f_id_μ)=multiply from i=1 to n multiply from i=1 to n(X_i)f_id_μ,其中fi(i=1,2,…,n)是Xi上任一有界连续函数.
基金Supported by the NSF of China(10571063)Supported by the NSF of Guangdong Province(05006515)
文摘In this paper,a necessary and sufficient condition of a measure to be the product Borel probability measure on the product space of some compact metric spaces are given.
基金supported by National Natural Science Foundation of China (Grant No. 11071054)the fund of Hebei Normal University of Science and Technology (Grant Nos. ZDJS2009 andCXTD2010-05)
文摘In this paper,we introduce the concept of measure-theoretic r-entropy of a continuous map on a compact metric space,and get the results as follows:1.Measure-theoretic entropy is the limit of measure-theoretic r-entropy and topological entropy is the limit of topological r-entropy(r → 0);2.Topological r-entropy is more than or equal to the supremum of 4r-entropy in the sense of Feldman's definition,where the measure varies among all the ergodic Borel probability measures.
