Let $(\mathbb{K},\mathfrak{M}_{\mathbb{K}})$ be an adelic field, $X$ a proper variety over $\mathbb{K}$ and ${\overline{L}}_{i}$, $i=0,\dots,d$, a family of integrable metrized line bundles on $X$. Let $Y$ be a $d$-dimensional cycle of $X$. We say that $Y$ is integrable with respect to ${\overline{L}}_{0},\dots,{\overline{L}}_{d}$ if there is a proper map $\varphi\colon X^{\prime}\to X$, a cycle $Y^{\prime}$ of $X^{\prime}$ such that $\varphi_{\ast}Y^{\prime}=Y$, and rational sections $s_{i}$ of $\varphi^{\ast}L_{i}$, $i=0,\dots,d$, that intersect $Y^{\prime}$ properly and such that for all but a finite number of $v\in\mathfrak{M}_{\mathbb{K}}$,

(2.54)

$$\operatorname{h}_{v,{\overline{\varphi}}^{\ast}L_{0},\dots,{\overline{\varphi}}^{\ast}L_{d}}(Y^{\prime};s_{0},\dots,s_{d})=0,$$

where $\operatorname{h}_{v}$ denotes the local height function on $X_{v}$.