We consider probability measures µ n , µ on a metric space X such that µ n weakly converges to µ. The following convergence lim n→∞ X f n (x)µ n (dx) = X f (x)µ(dx) is proved under some restrictions on real valued functions f n and f which are measurable, not necessarily continuous nor bounded.

this paper extends certain results of iglehart and whitt on multiple channel queues to the case where the inter-arrival times and service times are not necessarily identically distributed. it is shown that the weak convergence results in this case are exactly the same as those obtained by iglehart and whitt

In this paper, we study the problem concerning stability and asymptotic behaviours of solutions for a degenerate Landau-Lifshitz equation in micromagnetics involving only the nonlocal magnetostatic energy. Due to the lack of derivative estimates, we do not have the compactness needed for strong convergence and the natural convergence is weak* convergence. By formulating the problem in a new fra...