Some results on Complex $m-$subharmonic classes

In this paper we study the class $\mathcal{E}_{m}(Ω)$ of $m-$subharmonic functions introduced by Lu in \cite{L1}. We prove that the convergence in $m-$capacity implies the convergence of the associated Hessian measure for functions that belong to $\mathcal{E}_{m}(Ω)$. Then we extend those results to the class $\mathcal{E}_{m,χ}(Ω)$ that depends on a given increasing real function $χ$. A complete characterization of those classes using the Hessian measure is given as well as a subextension theorem relative to $\mathcal{E}_{m,χ}(Ω)$.

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