Proof of Useful Propositions as to Stochastic Convergence Proposition(a)LetfYYng be a sequence of n 1 random vectors withYYn d ! Y.SupposefXXng is a sequence of n 1 random vectors such that(XXn YYn) p ! 0Then XXn converges in distribution toYY. Proof Denote th...
Proof of Helly-Bray Theorem, Continuity Theorem and Cram´er -Wold Theorem Theorem(Helly-Bray)Let g(x) be bounded,continuous function and assume thatfFn(x)g is a sequence of uniformly bounded,non decreasing distribution functions which converges to F(x) at all ...