Assume $V$ is a compact $\mathbb{Q}$-CY Kähler space. Let $\Omega$ be a smooth Kähler metric on $V$. Then there is a unique semi-Kähler current with continuous potential and adapted Monge-Ampère measure $\Omega^{\prime}=\Omega+dd^{c}\varphi$, such that

where $\int_{V}\Omega^{n}=C\int_{V}(-1)^{n}v_{\alpha}$.

Furthermore, if $V$ is projective-algebraic and $[\Omega]\in NS_{\mathbb{R}}(V)$, then $\Omega+dd^{c}\varphi$ is smooth on $V^{reg}$ where it defines a bona fide Ricci flat metric.