Ex 1.1.9 in Tao's An introduction to measure theory asks us to show that any compact convex polytope in $\mathbb{R}^d$ is Jordan measurable. Is the following an efficient (or even valid) approach to the problem?
- Show that every $d$-dimensional solid simplex is Jordan measurable; and
- Show that any compact convex polytope in $\mathbb{R}^d$ can be expressed as a union of disjoint $d$-dimensional solid simplices.