The Monge-Ampère measure of any bounded $\omega$-psh is linearly bounded by the capacity. More precisely, if $u$ is an $\omega$-psh function such that $-M\leq u\leq 0$, where $M\geq 1$, then

$$\MA(u)\leq M^{n}\Capa_{\omega}$$

on Borel sets.