Let $X$ be a strictly $K$-analytic space and $L$ a line bundle on $X$, i.e. a locally free sheaf of rank 1 on the G-topology. A continuous metric $\|\cdot\|$ on $L$ is a function which asserts to any admissible open subset $U\subseteq X$ and any section $s\in\Gamma(U,L)$ a continuous (with respect to the Berkovich topology) function $\|s(\cdot)\|:U\rightarrow\mathbb{R}_{\geq 0}$ such that:

1. i)

   For an admissible open subset $V\subseteq U$ we have $\left\|s\Big|_{V}(\cdot)\right\|=\|s(\cdot)\|\Big|_{V}$,

2. ii)

   for $f\in\Gamma(U,\mathcal{O}_{X})$ we have $\|fs(\cdot)\|=|f(\cdot)|\|s(\cdot)\|$,

3. iii)

   for $p\in U$ we have $\|s(p)\|=0$ if and only if $s(p)=0$.

Given a formal model $(\mathfrak{X},\mathfrak{L})$ of $(X,L)$ one can define an associated so called formal metric $\|\cdot\|_{\mathfrak{L}}$ on $L$ in the following way: If $s$ is a local frame of $\mathfrak{L}$ on a formal open subset $\mathfrak{U}\subseteq\mathfrak{X}$ we define $\|fs(\cdot)\|_{\mathfrak{L}}=|f(\cdot)|$ on $\mathfrak{U}^{\textup{an}}$ for any $f\in\Gamma(\mathfrak{U}^{\textup{an}},\mathcal{O}_{\mathfrak{X}}^{\textup{an}})$. As this is independent of the choice of $s$ and $\mathfrak{X}^{\textup{an}}$ is covered by such sets, this gives a well-defined metric on $L$.