Let $L$ be an ample line bundle on $X$, ${\mathscr{L}}$ an extension to a model ${{\mathscr{X}}}$ and $\theta={c_{1}(L,{\|\ \|}_{\mathscr{L}})}\in\mathcal{Z}^{1,1}(X)$. For $m>0$ let

(2.3)

$${\mathfrak{a}}_{m}=\mbox{\rm Im}\,\bigl(H^{0}({{\mathscr{X}}},{\mathscr{L}}^{\otimes m})\otimes_{K^{\circ}}{\mathscr{L}}^{\otimes-m}\to{\mathcal{O}}_{{\mathscr{X}}}\bigr)$$

be the $m$-th base ideal of ${\mathscr{L}}$ and $\varphi_{m}:=m^{-1}\log|{\mathfrak{a}}_{m}|$. Then $\varphi_{m}\in{\rm PSH}_{\mathscr{D}}(X,\theta)$ and

(2.4)

$$\lim_{m\to\infty}\varphi_{m}=\sup_{m\in\mathbb{N}}\varphi_{m}={P}_{\theta}(0)$$

pointwise on $X^{\mathrm{an}}$.