Editing Smith–Volterra–Cantor set (section)

==Properties==

By construction, the Smith–Volterra–Cantor set contains no intervals and therefore has empty interior. It is also the intersection of a sequence of [[closed set]]s, which means that it is closed.
During the process, intervals of total length 
<math display=block>\sum_{n=0}^\infty \frac{2^n}{2^{2n + 2}} = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots = \frac{1}{2}\,</math> 
are removed from <math>[0, 1],</math> showing that the set of the remaining points has a positive measure of 1/2. This makes the Smith–Volterra–Cantor set an example of a closed set whose [[Boundary (topology)|boundary]] has positive [[Lebesgue measure]].