关于信息度量问题的思考

Thinking on the measurement problems of information

为克服Shannon熵的局限性,修改了Shannon熵的公理,用公理化的方法,推导出具有有限分布列的离散型随机变量的信息量系。并且将它推广到任意具有可数无限分布列的离散型随机变量和随机向量。证明了信息量系的最大信息量定理,可加性定理,广义可加性定理、互信息定理、独立性定理等性质。对信息量系中参数值的选取提出建议。

In order to eliminate the limitation of the Shannon entropy,the axiom system for the Shannon entropy was modified,and an information measure system with the axiomatization method was deduced.That could be extended to all discrete random variable and vector with the infinited countable distribution series.The paper proved the theorem of maximum information measure,the theorem of additivity,the theorem of generalized additivity,the theorem of mutual information measurement and the the theorem of independency.Suggestions to choose the value of the parameters in the information mearurement system were put forward.