Some remarks on the strong law of large numbers for Banach-space valued weakly integrable random variables |
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| Authors: | A. Bozorgnia M. Bhaskara Rao |
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| Affiliation: | 1. Meshed University Meshed, Iran;2. Sheffield University, Sheffield, United Kingdom |
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| Abstract: | The purpose of this paper is to show the equivalence of almost sure convergence of Sn/n, n ≥ 1 and lim supn→∞Sn/n < ∞ a.e., where Sn = X1 + X2 + … + Xn and X1, X2,… are independent identically distributed random elements in a separable Banach space with EX1 < ∞. This result disproves a result of Pop-Stojanovic [8]. |
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| Keywords: | Random elements in Banach spaces weak integrability strong law of large numbers |
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