Some results on the convergence of Hessian operator and $ m-$subharmonic functions

Abstract

<abstract><p>In this paper we treat the problem of connection between the convergence in $ m- $capacity and the convergence of the Hessian measure for a sequence$ f_j $ of $ m- $subharmonic functions. We prove first that, under some conditions, the convergence of $ f_j $ in capacity $ Cap_m $ implies the weak convergence of the Hessian measures $ H_m(f_j) $. Then we show that the converse sense of convergence is also true in some particular cases.</p></abstract>