关于可能性测度的扩张

本文讨论可能性测度的扩张理论。首先,我们引入了分别称之为ECP—系,CP—系的集类 B、B,并证明了文献中引入的一个集类D的所有原子族AD]是它们的特款。进一步,我们证明了可能性测度B(分别地,B)到U(B)(分别地,由B生成的广域或拓扑)上的扩张定理。

On the Extension of the Possibility Measures

In this paper, the theory of extension of the possibility measures is discussed, First, we introduce two classes B and B of sets called ECP-system and CP-system respectively , and prove that the c lassAD]of all atoms of a class D introduced in 1 , 2] must be ECP-system and CP-system. Furthermore, the Extension theorem from B (resp. B) to U(B)(resp. the plump field or the topology generated by B) of the possibilty measures is proved.