The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties. It applies this approach for the derivation of information inequalities with Shannon information measures. Connections of the considered approach to a generalized version of Shearer's lemma, and other related results in the literature are considered. Some of the derived information inequalities are new, and also known results (such as a generalized version of Han's inequality) are reproduced in a simple and unified way. In its second part, this paper applies the generalized Han's inequality to analyze a problem in extremal graph theory. This problem is motivated and analyzed from the perspective of information theory, and the analysis leads to generalized and refined bounds. The two parts of this paper are meant to be independently accessible to the reader.

翻译：本文件第一部分提出了一种统一的方法,用以计算满足亚/超模式特性的既定功能的不平等家庭,用香农信息措施来分析信息不平等,用香农信息措施来分析信息不平等,考虑对希勒勒勒勒勒姆马的通俗版的研究方法的关联,以及文献中的其他相关结果,一些衍生的信息不平等是新的,还以简单统一的方式复制已知的结果(如汉氏不平等的通俗版),第二部分运用普通汉的不平等来分析一个问题,从信息理论的角度对该问题进行激励和分析,分析导致普遍和完善的界限,这两部分旨在让读者可以独立查阅。