实变函数中集合外测度三种定义的等价性

Equivalence of Three Definitions about Exterior Measure in Real Variable Function

本文列出了实变函数中集合外测度的三个常见的定义,并对其之间的等价性给出了证明。通过这三种定义证明了外测度的一些基本性质,从而更好地揭示外测度这一概念的内涵。

In this paper, we set out three ordinary definitions of exterior measure and prove their mutual equivalence. In ad- dition,we prove some exterior measuro~ basic properties by using the three definitions. So the concept essence of exterior measure can be better showed.