Abstract
The aim of this paper is to study the existence of a solution to the complex Hessian equation associated to an m-positive closed current T. We give a sufficient condition on T and the measure mu so that the equation T Lambda beta(n-m) Lambda (dd(c).)(m-p) = mu has a solution on the set of m-subharmonic functions. For this we establish a connection between the convergence in cap(m,)(T) of a sequence of m-subharmonic functions and the weak convergence of the associated Hessian measure.