Abstract
Let {Vn, n ≥ 1} be a sequence of random elements in a real separable Banach space and suppose that {Vn, n ≥ 1} is stochastically dominated by a random element V. Let {an, n ≥ 1} and {bn, n ≥ 1} be real sequences with 0 < bn ↑ ∞. Conditions are provided under which {anVn, n ≥ 1} obeys the general strong law of large numbers almost surely irrespective of the joint distributions of the {Vn, n ≥ 1}. No geometric conditions are imposed on the underlying Banach space. Examples are provided which illustrate, compare, or demonstrate the sharpness of the results.
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