Solutions of semi-linear stochastic evolution integro-differential inclusions with Poisson jumps and non-local initial conditions

In this paper, we mainly investigate properties on solution sets of a semi-linear stochastic evolution integro-differential inclusion with Poisson jumps and non-local initial conditions. We firstly establish the existence of solutions to the addressed equation via weak topology technique. Through establishing the estimate on noncompactness measure of integrals for Poisson jumps, we further show that the solution set is a compact Rδ-set when the resolvent operator is compact or non-compact, respectively.