Let $S=\{x_{1},...,x_{N}\}\subset X^{\mathrm{div}}$ be a finite set of divisorial points and let $\mu$ be a positive Radon measure of mass $\{\omega\}^{n}$ with support contained in $\{x_{1},...,x_{N}\}$. Then there exists $t\in\mathbf{R}^{N}$ such that the function $\varphi_{S,t}$ defined by (8.4) solves $\MA(\varphi_{S,t})=\mu$.