This paper studies an impulsive dynamical system that is in the form of a measuredriven diff.erential inclusion. The employed solution concept depends upon a graph completion of the measure. The.first main result shows that a subsequence of discrete- time trajectories graph- converges to a solution, and, under Lipschitz hypotheses, that every solution can be obtained in this manner. The second main result pursues a similar development with classical systems that approximate the given one.