On the Strong Law of Large Numbers for Sums of Independent Banach Space Valued Random Elements

Cantrell, Amy; Rosalsky, Andrew

doi:10.1081/sap-120006105

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2003

2009

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“…3.1) established a SLLN for a compactly uniformly integrable sequence of independent random elements, by using a result in (Cantrell and Rosalsky, 2002) which was stated for a sequence of random elements {V n , n ≥ 1} in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space. We also obtain a result (Corollary 3) very close to the one from Cantrell and Rosalsky (2004) without requiring the condition of compactly uniform integrability and without any condition of independence among the random elements.…”

Section: Accepted M Manuscriptmentioning

confidence: 99%