Let $\Delta$ be a lattice polytope of $M_{\mathbb{R}}$. Then the subset of rational piecewise affine concave functions in ${\overline{\mathscr{P}}}(\Delta,N_{\mathbb{R}})$ (respectively, in ${\overline{\mathscr{P}}}(N_{\mathbb{R}},\Delta)$) is dense with respect to uniform convergence.