  The complex Monge-Amp\`ere operator $(dd^c)^n$ is an important tool in
complex analysis. It would be interesting to find the right notion of
convergence $u_j\to u$ such that $(dd^cu_j)^n\to (dd^cu)^n$ in the weak
topology. In this paper, using the $C_{n-1}$-capacity, we give a sufficient
condition of the weak convergence $(dd^cu_j)^n\to (dd^cu)^n$. We also show that
our condition is quite sharp in some case.
