Let $V$ be a strictly $K$-analytic Hausdorff space of dimension $n$ and $\overline{L}_{1},...,\overline{L}_{n}$ semipositive piecewise $\mathbb{Q}$-linear metrized line bundles on $V$. The assignment

	$\displaystyle C_{c}(V)$	$\displaystyle\rightarrow\mathbb{R}_{\geq 0},$
	$\displaystyle f$	$\displaystyle\mapsto\frac{1}{e_{1}\cdot...\cdot e_{n}}\int_{W}f\;c_{1}\left(\overline{L}_{1}^{e_{1}}\Big|_{W}\right)\wedge...\wedge c_{1}\left(\overline{L}_{n}^{e_{n}}\Big|_{W}\right)$

where $W$ is a compact strictly $K$-analytic domain with $\supp(f)\subseteq\overset{\circ}{W}$ and $e_{1},...,e_{n}\in\mathbb{N}$ are non-zero integers such that $\overline{L}_{i}^{e_{i}}\Big|_{W}$ is a formally metrized line bundle, yields a positive linear functional on the space $C_{c}(V)$ of continuous functions with compact support in $V$ and hence by the Riesz Representation Theorem (see [Rud87, Theorem 2.14]) a positive Radon measure on $V$ which we again denote by $c_{1}(\overline{L}_{1})\wedge...\wedge c_{1}(\overline{L}_{n})$. Note that the integral does neither depend on the choice of $W$ by Lemma 4.8 nor on the choice of the $e_{i}$ by Proposition 4.5 and that we can always find such a $W$ together with the $e_{i}$ by choosing for every point in $\supp(f)$ a compact strictly $K$-analytic neighbourhood where some powers of the $\overline{L}_{i}$ are formally metrized and using compactness of $\supp(f)$.