Let ${\|\hskip 4.30554pt\|}$ be a piecewise ${\mathbb{Q}}$-linear metric on the line bundle $L$ over $V$ and let $x\in V$. Then ${\|\hskip 4.30554pt\|}$ is called semipositive in $x\in V$ if and only if we may choose a compact strictly $K$-analytic domain $W$ which is a neighbourhood of $x$ and some integer $k\geq 1$ such that ${\|\hskip 4.30554pt\|}_{|W}^{\otimes k}$ is a semipositive formal metric.