Abstract
Let \({\{X_n, n \geq1 \}}\) be a sequence of random variables and {bn, n ≥ 1} a nondecreasing sequence of positive constants. No assumptions are imposed on the joint distributions of the random variables. Some sufficient conditions are given under which \({\lim_{n\to \infty}\sum_{i=1}^n X_i/b_n=0}\) almost surely. Necessary conditions for the strong law of large numbers are also given.
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