An alternative way to define the Cantor set is the following:
![\[\mathfrak{C}=[0,1] \setminus \bigcup_{n=1}^\infty \;\bigcup_{k=0}^{3^{n-1}-1} \left(\frac{3k+1}{3^n},\frac{3k+2}{3^n}\right)\]](https://www.math.tolaso.com.gr/wp-content/ql-cache/quicklatex.com-83c785884e4493ca4065020ab9d8cf6b_l3.png "Rendered by QuickLaTeX.com")
What is the Lebesgue measure of the Cantor set if we consider it as a subset of 
? Is 
countable?
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An alternative way to define the Cantor set is the following:
What is the Lebesgue measure of the Cantor set if we consider it as a subset of ? Is countable?