20.21. Suppose that the sequence (X) is fundamental in probability in the sense that for e positive there exists an N such that P[IX-X|>e] N. (a) Prove there is a subsequence (X) and a random variable X such that lim XX with probability 1. Hint: Choose increasing n such that P[IX-X,>2-k]<2-k for m, nzn. Analyze P[IX-Xn>2-k]. (b) Show that X₁ →p X.

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