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
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.
