Existence and stability of solutions of general semilinear elliptic equations with measure data

We study existence and stability for solutions of $Lu+g(x;u)=\omega$ in the closure of open set $\mathrm{\Omega }$ where L is a second order elliptic operator, $g$ a Caratheodory function and $\omega$ a measure in $\bar{\mathrm{\Omega }}$. We present a uni ed theory of the Dirichlet problem and the Poisson equation. We prove the stability of the problem with respect to weak convergence of the data.