Weak convergence of Monge-Ampère measures on compact Hermitian manifolds

We give a sufficient condition on a sequence of uniformly bounded \(\omega\)-plurisubharmonic functions, \(\omega\) being a Hermitian metric, for which the sequence of associated Monge-Ampère measures converges weakly. This criterion can be used to obtained a bounded \(\omega\)-plurisubharmonic solution to the Monge-Ampère equation.