Let $Y$ be a $d$-dimensional cycle of $X$, ${\overline{L}}_{i}=(L_{i},\|\cdot\|_{i})$, $i=0,\dots,d$, a collection of integrable metrized line bundles, and $s_{d}$ a rational section of $L_{d}$ such that $\operatorname{div}(s_{d})$ intersects $Y$ properly. Then $\log\|s_{d}\|$ is integrable with respect to the measure $\operatorname{c}_{1}({\overline{L}}_{0})\land\dots\land\operatorname{c}_{1}({\overline{L}}_{d-1})\wedge\delta_{Y}$.