Abstract
For a sequence of identically distributed random variables { X n , n ≥ 1 } with partial sums S n = ∑ i = 1 n X i , n ≥ 1 and a sequence of positive constants { b n , n ≥ 1 } with b n ↗ ∞ , conditions are provided under which the strong law of large numbers S n / b n → 0 almost surely holds irrespective of the joint distributions of the { X n , n ≥ 1 } . It is not assumed that E | X 1 | < ∞ . Illustrative examples are provided which compare the results obtained with other results in the literature.
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