Let us again consider an open subset $W$ of ${X^{\rm an}}$. A function $f:W\rightarrow{\mathbb{R}}\cup\{\pm\infty\}$ is called locally integrable if $f$ is integrable with respect to the measure $\mu$ associated to any $\omega\in A_{c}^{2n}(W)$. Then we write $\int_{W}f\omega:=\int_{W}fd\mu$.

For a locally integrable function $f$ on $W$ and $\eta\in A^{p,q}(W)$, we define $[f\cdot\eta]\in D_{p,q}(W)$ by $[f\cdot\eta](\alpha):=\int_{W}f\eta\wedge\alpha$ for every $\alpha\in A_{c}^{n-p,n-q}(W)$.