  We discuss the homogeneous Dirichlet problem for $p$-Poisson type equations
with locally finite measure data. If there is a H\"{o}lder continuous solution,
the corresponding data satisfies a local Morrey type condition. The main result
of this paper provides existence of a global H\"{o}lder continuous solution
under the same condition. The existence result gives a compact embedding
theorem. Our results are also new even for the Poisson equation.
