Let $C\subset N_{\mathbb{R}}$ be an open convex set and $||\cdot||$ any fixed norm on $M_{\mathbb{R}}$. A differentiable concave function $f\colon C\to\mathbb{R}$ is of Legendre type if it is strictly concave and $\lim_{i\to\infty}\|\nabla f(u_{i})\|\to\infty$ for every sequence $(u_{i})_{i\geq 1}$ converging to a point in the boundary of $C$. In particular, any differentiable and strictly concave function on $N_{\mathbb{R}}$ is of Legendre type.