On Some Weighted Classes of m-Subharmonic Functions

In this paper, we study the class E m () of m-subharmonic functions introduced by Lu in [18].We prove that the convergence of the Hessian measures is deduced from the convergence in m-capacity for the functions that belong to E m () satisfying certain additional properties.Then we extend those results to the class E m, () that depends on a given increasing real function .A complete characterization of those classes using the Hessian measure is given as well as a subextension theorem relative to E m, ().