Let $\mathscr{X}$ be an algebraic scheme over $K^{\circ}$, $\mathfrak{a}$ a vertical coherent fractional ideal sheaf on $\mathscr{X}$ (i.e. $\mathfrak{a}$ is a coherent subsheaf of the sheaf of total quotient rings $\mathcal{K}_{\mathscr{X}}$ such that after multiplying with some element of $K^{\circ}\setminus\{0\}$ it becomes a vertical ideal sheaf) and $\red:\mathscr{X}^{\textup{an}}\rightarrow\tilde{\mathfrak{X}}$ the reduction map. We define the function $\log|\mathfrak{a}|:\mathscr{X}^{\textup{an}}\rightarrow\mathbb{R}$ by $\log|\mathfrak{a}|(x):=\sup\left\{\log|f(x)|\;\Big|\;f\in\mathfrak{a}_{\red(x)}\right\}$. The supremum is actually a maximum as for a set of generators $f_{1},...,f_{r}$ of $\mathfrak{a}_{\red(x)}$ we have $\sup\left\{\log|f(x)|\;\Big|\;f\in\mathfrak{a}_{\red(x)}\right\}=\max\left\{\log|f_{i}(x)|\;\Big|\;1\leq i\leq r\right\}$.