Convergence in $(\omega ,m)$-capacity in the class $\mathcal{E}(X,\omega ,m)$ on compact Kähler manifolds

In this paper, we establish the weak*-convergence of a sequence of the complex Hessian measures $H_m(u_j)$ to the complex Hessian measure $H_m(u)$ in the class $\mathcal{E}(X,\omega ,m)$ under hypotheses that $u_j$ is convergent to $u$ in $(\omega ,m)$-capacity.