Suppose a1, a2,... is a sequence of real numbers with an → ∞. If $\lim \sup(X_1 + \cdots + X_n)/a_n = \alpha$ a.s. for every sequence of independent nonnegative uniformly bounded random variables X1, ...

This is a preview. Log in through your library . Abstract For each $k = 1, 2, \cdots$ let $n = n(k)$, let $m = m(k)$, and suppose $y_1^k, \cdots, y_n^k$ is an $m ...