Some remarks on the strong law of large numbers for Banach-space valued weakly integrable random variables

The purpose of this paper is to show the equivalence of almost sure convergence of Sn/n, n >= 1 and lim supn-->[infinity]||Sn||/n < [infinity] a.e., where Sn = X1 + X2 + ... + Xn and X1, X2,... are independent identically distributed random elements in a separable Banach space with E||X1|| < [infinity]. This result disproves a result of Pop-Stojanovic [8].

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Year of publication:	1978
Authors:	Bozorgnia, A. ; Rao, M. Bhaskara
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 8.1978, 4, p. 579-583
Publisher:	Elsevier
Keywords:	Random elements in Banach spaces weak integrability strong law of large numbers

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005093905