Lemma 5.2 . [00SL]

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Lemma 5.2.

Let $u$ be a bounded convex function on the square $\{|x_{i}|<1\}\subset\mathbb{R}^{n}$ . Via the rescaled log map $s^{-1}\text{Log}:(\mathbb{C}^{*})^{n}\to\mathbb{R}^{n}$ , the function $u$ pulls back to a psh function on $\{|\log|z_{i}||<s\}$ . Then the real MA measure of $u$ is related to the pushforward of the complex MA measure of $u\circ s^{-1}\text{Log}$ by

MA(u)=\frac{s^{n}}{\pi^{n}n!}(s^{-1}\text{Log})_{*}(\sqrt{-1}\partial\bar{\partial}(u\circ s^{-1}\text{Log}))^{n}.