  The purpose of this paper is to study stochastic evolution inclusions of the
form \begin{align*}
  \eta(t,z) N_{\Theta}(dt \otimes z)\in dX(t)+\mathcal{A} X(t)dt, \end{align*}
where $\mathcal{A}$ is a multi-valued operator acting on a separable Banach
space and $N_{\Theta}$ is the counting measure induced by a point process
$\Theta$. Firstly, we will set up the concepts of strong and mild solutions;
then we will derive existence as well as uniqueness criteria for these kinds of
solutions and give a representation formula for the solutions. The results will
be formulated by means of nonlinear semigroup theory and except for
separability, no assumptions on the underlying Banach space are required.
