Proof of Useful Propositions as to Stochastic Convergence
 Proof of Useful Propositions as to Stochastic Convergence

Let Y_n be a sequence of n×1 random vectors with
Y_n →Y in distribution. Suppose X_n is a sequence of
n×1 random vectors such that (X_n-Y_n)→0 in probability. Then X_n converges in distribution to Y.

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