  Let $u$ be a maximal plurisubharmonic function in a domain
$\Omega\subset\mathbb{C}^n$ ($n\geq 2$). It is classical that, for any
$U\Subset\Omega$, there exists a sequence of bounded plurisubharmonic functions
$PSH(U)\ni u_j\searrow u$ satisfying the property: $(dd^c u_j)^n$ is weakly
convergent to $0$ as $j\rightarrow\infty$. In general, this property does not
hold for arbitrary sequence. In this paper, we show that for any sequence of
bounded plurisubharmonic functions $PSH(U)\ni u_j\searrow u$, $(|u_j|+1)^{-a}
(dd^cu_j)^n$ is weakly convergent to $0$ as $j\rightarrow\infty$, where
$a>n-1$. We also generalize some well-known results about approximation of
maximal plurisubharmonic functions.
