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1Topological r-entropy and measure-theoretic r-entropy of a continuous map显示文摘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.REN YunLi HE LianFai LV JinFeng ZHENG GuoPing 2011Science China Mathematics2011,54,6:5
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