Consider that a subset $A$ of $\mathbb{R}^{n}$ has measure $0$ if for every $\epsilon > 0$, there is a cover $\{U_{1}, U_{2}, \cdots \}$ of $A$ by closed (or open) rectangles such that $$\sum_{i = 1}^{\infty}v(U_{i}) < \epsilon$$
With this definition, I'd like to prove that de boundary of a disc has zero measure. Thank you in advance.