无序和的一个注记

One Note of Unordered Sums

对于任意集合上广义实数取值的非负函数,文献[1]给出了无序和的两种定义,文献[2]给出了无序和的第三种定义,文章证明了这三种定义相互等价.对于任意集合上绝对可和的复值函数,文献[1]和文献[2]分别给出了无序和的两种不同定义,文章证明了这两种定义等价.

For an extended real valued non negative function on an arbitrary set.Two different definitions of the unordered sum were given in[1].A third definition of the unordered sum was given in[2],the equivalence of the three definitions was proved in this article.For an complex valued function on an arbitrary set,two different definitions of the unordered sum were separately given in[1]and[2],the equivalence of the two definitions was proved in this article.