Let $a : [0,T] \to \mathbb{R}$ be càdlàg and in $BV[0,T]$, and let $h \in L^1([0,T], |da|)$. Then \begin{align*} \left| \int_0^T h(s)\, da(s) \right| \leq \int_0^T |h(s)|\, |da(s)|. \end{align*} The process $h \cdot a : [0,T] \to \mathbb{R}$ defined by $(h \cdot a)(t) = \int_0^t h(s)\, da(s)$ is càdlàg and in $BV[0,T]$, with associated signed measure $h(s)\, \mu(ds)$. Moreover, $|h(s)\, da(s)| = |h(s)|\, |da(s)|$ as measures.