Let $\pi:X\to V$ be a resolution of $V$. We may define a semipositive big smooth form on $X$ by $\omega=\pi^{*}\Omega$. By Theorem 2.1 and Proposition 3.1 we can solve uniquely $(\omega+dd^{c}\bar{\varphi})^{n}=f\circ\pi\omega^{n}$ where $\bar{\varphi}$ is a continuous function on $X$ such that $\omega+dd^{c}\bar{\varphi}$ is semipositive. Let $F$ be a fiber of $\pi$ and $i:F\to X$ the inclusion map. $F$ is connected by Zariski’s main theorem. Furthermore $i^{*}\omega+dd^{c}i^{*}\bar{\varphi}$ is semipositive on $F$. Since $i^{*}\omega=0$, it follows that $i^{*}\varphi$ is a continuous psh function on $F$. Hence $i^{*}\bar{\varphi}$ is constant. This implies that $\bar{\varphi}=\varphi\circ\pi$ where $\varphi$ is a continuous function on $V$. We do have $(\Omega+dd^{c}\varphi)^{n}=f\Omega^{n}$. ∎