不可测集的性质

Some properties of unmeasurable sets

研究了不可测集的性质:如果一列互不相交的集合并集的外测度小于外测度的和,则其中至少有两个是不可测集。通过具体例子说明:存在一列互不相交的不可测集使得它们并集的外测度小于外测度的和。

Some properties of unmeasurable sets are studied.It is shown if the outer measune of a countable union of disjoint sets is less than the sum of the outer measures of these sets,then there exist at least two sets of them which are unmeasurable.A example is given for this conclusion.