# Thread: Cantor Set in Measure Theory

1. ## Cantor Set in Measure Theory

This thesis is a survey for the using of Cantor sets and in measure theory. It is proved that and are measurable and have zero measure. Following that it is shown that the measure of is positive and the measure of is zero. Also it is shown that there exists a subset of such that is non measurable. At the end of this thesis it is shown that there is no subset such that is Bernstein in .