Convex function almost surely differentiable.

If f: $\mathbb{R}^n \rightarrow \mathbb{R}$ is a convex function, i heard that f is almost everywhere differentiable. Is it true? I can't find a proof (n-dimentional).

Thank you for any help

For a proof that doesn't rely directly on the Rademacher theorem, try Rockafellar's "Convex analysis", Theorem 25.5.

From the book: Let $f$ be a proper convex function on $\mathbb{R}^n$, and let $D$ be the set of points where $f$ is differentiable. Then $D$ is a dense subset of $(\operatorname{dom} f)^\circ$, and its complement is a set of measure zero. Furthermore, the gradient mapping $x \mapsto \nabla f(x)$ is continuous on $D$.