# Statement of the $d d^c$-Lemma

I'm looking at the definition of Green's function $g_\mu$ for the Laplacian $\Delta_\mu$ associated to a positive $(1,1)$-form $\mu$ on a Riemann Surface $X$.

In specific the main request that the function $g_\mu:X \times X \rightarrow \mathbb{R}\cup \{\infty\}$ must satisfy is the following equation of $(1,1)$-forms:

$$dd^c g_\mu(w,z) + \delta_w(z)=\frac{\mu(z)}{Vol_\mu(X)}.$$

I'm confused about the meaning of the first term (also of the second, but it is another question). Googling around I found post referrings to the $dd^c$-Lemma (For example on Math.Overflow there are many), but I didn't find neither a statement nor a proof. Since I think it could be useful to understand (and to use in relation to) the formula above I would like to have a precise reference for it.