Cantor Set has Zero Lebesgue Measure

Theorem
Let $\mathcal C$ be the Cantor set.

Let $\lambda$ be the Lebesgue measure on the Borel $\sigma$-algebra $\mathcal B \left({\R}\right)$ on $\R$.

Then $\mathcal C$ is $\mathcal B \left({\R}\right)$-measurable, and $\lambda \left({\mathcal C}\right) = 0$.

That is, $\mathcal C$ is a $\lambda$-null set.