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We give a sufficient condition on a sequence of uniformly bounded$\omega$-plurisubharmonic functions, $\omega$ being a Hermitian metric, forwhich the sequence of associated Monge-Amp\`ere measures converges weakly. Thiscriterion can be used to obtained a bounded $\omega$-plurisubharmonic solutionto the Monge-Amp\`ere equation.

Weak convergence of Monge-Amp\`ere measures on compact Hermitian manifolds