PLease can you help me to prove the following theorem,
Let Fn(u) denote the distribution function of a random variable Un whose distribution depends upon the positive integer n. Let F(u) the limiting distribution of Un. Let Vn be a random variable that converges in probabiity , then
Un/Vn=Wn converges in distribution to zero. that is, the limiting distribution of Wn is the same that the limiting distribution of Un , F(w)
Thank you