共轭可交换性及其在集合形式单调类定理中的应用  

Conjugate Interchangeabilty and Its Applications in the Theory of Monotone Class Theorem of Set Form

作　　者：徐远[1] 

机构地区：[1]海南师范大学数学与统计学院,海南海口571158

出　　处：《数学的实践与认识》2014年第12期299-305,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11261016)

摘　　要：引入了集列的极限运算与二元集运算之间的共轭可交换性的概念,讨论了常见的和重要的集列的极限运算与集代数运算之间所具有的共轭可交换性质,在一般的情形下证明了共轭可交换性是集类的极限运算生成类对集代数运算具有封闭性的一个充分条件,使得集合形式的单调类定理的理论得到了统一的解释,并且证明更简单,思路更清晰,最后还给出了一个新的集合形式的单调类定理.In this paper, the concept of conjugate interchangeabilty between the limit operations on set sequences and the dualistic set operations is introduced, the conjugate interchangeabilty of some familiar and important limit operations on set sequences and the dualistic set operations is discussed, and under very general condition this property is proved to be a sufficient condition of the close of finite set operations on the generation by limit operations of set class, which makes the the monotone class theorems of set form are interpreted by unified method with more simple proof and more clear thread, in the last of this paper, a new monotone class theorem of set form is given.

关 键 词：共轭可交换性 单调类定理 集列的极限运算 集类的生成类 δ类 

分 类 号：O144[理学—数学]