Let $X$ be a separated scheme of finite type over $K$ of dimension $n$ with line bundles $L_{1},...,L_{n}$ on $X$. Let $V$ be an open subset of $X^{\textup{an}}$ and $\|\cdot\|_{i}$ a continuous metric on $L_{i}^{\textup{an}}\Big|_{V}$ for each $i$. Denote by $\overline{L}_{1},...,\overline{L}_{n}$ the line bundles $L_{1}^{\textup{an}}\Big|_{V},...,L_{n}^{\textup{an}}\Big|_{V}$, endowed with these metrics. For $i\in\{1,...,n\}$ let $(\|\cdot\|_{i,k})_{k\in\mathbb{N}}$ be piecewise $\mathbb{Q}$-linear metrics on $L_{i}\Big|_{V}$ converging uniformly to the continuous metric $\|\cdot\|_{i}$ on $L_{i}\Big|_{V}$. Suppose that all $\|\cdot\|_{i,k}$ are semipositive in $V$. Denote by $\overline{L}_{i,k}$ the line bundle $L_{i}^{\textup{an}}\Big|_{V}$ endowed with the metric $\|\cdot\|_{i,k}$. Then the measures $c_{1}\left(\overline{L}_{1,k}\right)\wedge...\wedge c_{1}\left(\overline{L}_{n,k}\right)$ converge weakly to a positive Radon measure on $V$.