So I have proved that a compact, convex polytope is Jordan measurable at the heed of Terrance Tao's "Introduction to measure theory" Exercise 1.1.9. My current question is how to expand this to the general compact polytope?
I could imagine a proof going something like let $P$ be a polytope and let $B=\{E\subseteq P|E $ is convex and open$ \}$. $B$ covers $int(P)$, and it feels like we could somehow $int(P)$ had a finite cover due to compactness, but I can't see how?
If you could expand on my attempt or provide there own I would be thrilled, thanks.