摘要
In this paper, some properties of the monotone set function defined by theChoquet integral are discussed. It is shown that several important structural characteristics of theoriginal set function, such as weak null-additivity, strong order continuity, property (s) andpseudomelric generating property, etc., are preserved by the new set function. It is also shown thatC-integrability assumption is inevitable for the preservations of strong order continuous andpseudometric generating property.
讨论了Choquet积分定义的单调集函数的几个遗传性质 .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 .最后通过 2个例子说明了当被积函数不是C可积时 。
