Yeah, and we have more than measure zero -- the subsets of the input space on which a fully ReLU MLP is linear are Boolean combinations of hyperspaces. I was coming at it from the heuristic that if you can triangulate a space into a finite number of easily computable convex sets such that the inside of each one has some trait, then it's as good as saying that the space has this trait. But of course this heuristic doesn't always have to be true, or useful.