In the situation of Theorem 5.2 we denote by $\overline{\mathcal{O}}^{h\circ p_{\mathfrak{X}^{\prime}}}$ the trivial line bundle on $\mathfrak{X}^{\prime\textup{an}}$ together with the metric which is given by $\|1\|=e^{-h\circ p_{\mathfrak{X}^{\prime}}}$. After base change to the completion of an algebraic closure $\mathbb{C}_{K}$ of $K$ this becomes a formally metrized line bundle by Proposition 2.11. So similarly as in Remark 4.16 we can define its non-archimedean Monge-Ampère measure by base change to $\mathbb{C}_{K}$.