(Yau). Let $X$ be a compact Kähler manifold of complex dimension $n$ and let $\chi$ be a Kähler class. Then for any smooth density $v>0$ on $X$ such that $\int_{X}v=\int_{X}\chi^{n}$ there exists a unique $($smooth$)$ Kähler metric $\omega\in\chi$ such that $\omega^{n}=v$.