This is probably fairly elementary, but does someone know how to prove the following or know a reference.

Let $X$ be a Kaehler manifold. Let $\theta$ be a closed $(1,1)$-form and $T$ be a closed positive $(1,1)$-current cohomologous to $\theta$. Then there is a quasi-plurisubharmonic function $\psi$ so that

$$ T=\theta +dd^c \psi.$$