Abstract
1. Introduction. Let {Xk: k ≥ 1} be a sequence of independent, but not necessarily identically distributed, random variables. Suppose that the random variables Xn are uniformly bounded by a random variable X in the sense that(1) P(|Xn| ≥x) ≤ P(|X| ≥ x)for all x > 0. Write qn(x) = P(|Xn| ≥ x) and q(x) = P(|X| ≥ x).
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