Let $(\varphi_{j})_{j}$ be a uniformly bounded net of $\omega$-psh functions, and assume that $\MA(\varphi_{j})$ converges to $\MA(\varphi)$ in the weak sense of measures for some bounded $\omega$-psh function $\varphi$. Then

$$\int h\MA(\varphi_{j})\to\int h\MA(\varphi)\quad\text{as $j\to\infty$}$$

for every bounded, quasicontinuous function $h$.