利用群作用构造一类不可测集

A Class of Non-Measurable Sets Is Constructed by Using Group Action

摘要: 本文研究了群作用和Zermelo选择公理构造出一类一维不可测集，为了得到主要结果，进行了n维不可测集的构造，在群作用和Zermelo选择公理的前提下，用构造的方法给出了n维不可测集，从而证明了一类n维不可测集的存在性，且给出了该类型不可测集的内侧度为零。

Abstract: In this paper, a class of one-dimensional unmeasurable sets is constructed by studying group action and Zermelo choice axiom. In order to get the main result, the dimensional unmeasurable sets are constructed. Under the premise of group action and Zermelo choice axiom, the dimensional unmeasurable sets are given by constructing method, thus proving the existence of a class of dimensional unmeasurable sets. The inner degree of this type of unmeasurable set is zero.