In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions. We prove existence of solutions and study properties of the solution set. It is also indicated how these results can be used in the study of control systems driven by vector measures.

We consider the stochastic differential equation (1) $du\left(t\right)=a(u\left(t\right),\xi \left(t\right))dt+{\int }_{\Theta }\sigma {(u\left(t\right),\theta )}_p(dt,d\theta )$ for t ≥ 0 with the initial condition u(0) = x₀. We give sufficient conditions for the existence of an invariant measure for the semigroup ${P^t}_{t\ge 0}$ corresponding to (1). We show that the existence of an invariant measure for a Markov operator P corresponding to the change of measures from jump to jump implies the existence of an invariant measure for the semigroup ${P^t}_{t\ge 0}$ describing the evolution of measures along trajectories and vice versa.