摘要
现代概率论是一门非常抽象的学科,其中的一些定理的证明过程非常复杂,有些教材只写出了部分过程,而舍掉了部分推导过程,导致了证明的不完整。本文对σ可加集函数分解定理证明过程进行详细分析,将抽象的表达式具体化,先研究简单的特殊情况,再利用归纳的方法推广到一般的情形。
Modern probability theory is a very abstract subject.The process of proving some of its theorems is very complex.Some textbooks only write part of the process,but give up part of the derivation process,which leads to the incomplete proof.In this paper,the proof process of decomposition theorem ofσadditive set function is analyzed in detail.The abstract expression is concretized,the simple special case is studied first,and then the method of induction is extended to the general case.
