摘要
Shannon’s information measure is a crucial concept in Information Theory. And the research, for the mathematics structure of Shannon’s information measure, is to recognize the essence of information measure. The linear relation between Shannon’s information measures and some signed measure space by using the formal symbols substitution rule is discussed. Furthermore, the coefficient matrix recurrent formula of the linear relation is obtained. Then the coefficient matrix is proved to be invertible via mathematical induction. This shows that the linear relation is one-to-one, and according to this, it can be concluded that a compact space can be generated from Shannon’s information measures.
Shannon＇ s information measure is a crucial concept in Information Theory. And the research, for the mathematics structure of Shannon＇ s information measure, is to recognize the essence of information measure. The linear relation between Shannon＇ s information measures and some signed measure space by using the formal symbols substitution rule is discussed. Furthermore, the coefficient matrix recurrent formula of the linear relation is obtained. Then the coefficient matrix is proved to be invertible via mathematical induction. This shows that the linear relation is one-to-one, and according to this, it can be concluded that a compact space can be generated from Shannon＇ s information measures.
基金
the Science and Technology Research Project of Education Department, Heilongjiang Province (Grant No.11513095)
the Science andTechnology Foundation of Heilongjiang Institute of Science and Technology(Grant No.04 -25).
关键词
香农信息测度
信息论
数学结构
矩阵表示法
entropy
Shannon＇s information measures
signed measure
the recurrent formula of l-measure matrix
