Green's formula for the non-weighted pluricomplex energy

Let $dV$ be a probability measure on $\mathbb{C}^{n}$ satisfying the assumptions stated before the conjecture, and let $E(dV)$ be its non-weighted pluricomplex energy. Energy Green-formula conjecture.

$$E(dV)=\lim_{k\to\infty}\frac{1}{kN_k}\int_{(\mathbb{C}^{n})^{N_k}}\log\left|D^{(N)}(z_1,z_2,\ldots,z_{N_k})\right|^2dV^{\otimes N_k}.$$

The source states that this formula would imply the preceding Green's-formula conjecture; it does not provide a resolution.