ScalingStacks

Proof. If $u$ is smooth, then

$$MA(u)(K)=\int_{K}\det(D^{2}u)dx_{1}\ldots dx_{n}=\frac{s^{n}}{\pi^{n}n!}\int_{(s^{-1}\text{Log})^{-1}(K)}(\sqrt{-1}\partial\bar{\partial}(u\circ s^{-1}\text{Log}))^{n}.$$

Since $u\in C^{0}$, and both the real and complex MA operators are weakly continuous with respect to $C^{0}$-limits, this equality passes to general $u$. ∎