How to display that the boundary of sphere is zero measure?
Do I perhaps need to enclose the sphere into a cube or rectangle? Since there are theorems:
If $A \subset \mathbb{R}^n$ is $n$- measure zero and $B \subset A$, then $B$ is $n$- measure zero.
The boundary of a compact interval $I \subset \mathbb{R}^n$ is $n$- measure zero.
I also think that I could make the sphere a subset of the intersection of $n$ intervals. E.g. in $\mathbb{R}^3$ I could make a cube $[a,b] \times [c,d] \times [e,f]$ and then use the second theorem above after which the first.