the concept of convergence of measures depends on the context. Do you mean narrow convergence, vague convergence, weak-convergence? Are you working in a locally compact Hausdorff space?
I am hoping someone could explain this concept to me.
and why we need to deine the borel sigma field on the set in the underlying metric space and then define a set of all finite boorel measures P(X) on the set B(X) in order to adequately describe convergence of measures