Let $f:\mathbb{R}\to \mathbb{R}$ be any Lipschitz function. We know that it is differentiable almost everywhere (which is basically Radamacher's Theorem in one -dimension). I want to prove the Radamacher's theorem in dimension $n$. The proof that I was reading can be found here. On page 21, it is written that using Fubini's theorem we conclude that the directional derivative of $f$ in the direction $v$ exists a.e.
I am unable to understand how Fubini's theorem is applied here to make this conclusion.