It is shown that several important structural characteristics of the original set function, such as weak null additivity, strong order continuity, property (s) and pseudometric generating property, etc. , are preserved by the new set function.

• 证明了Choquet积分定义的新的单调集函数遗传了原来集函数的几个重要的结构特性 ；如弱零可加性、强序连续性、性质 (S)和伪距离生成性质等 .