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On relatively uniform convergence of weighted sums of B-lattice valued random elements. (English) Zbl 1016.60004
Some interesting versions of the strong law of large numbers for Banach lattice-valued random variables, under hypotheses which are weaker than the classical ones, are proved. In this context the property of regularity, assumed in general in the literature, is dropped, and only $$\sigma$$-Dedekind completeness together with $$\sigma$$-property is supposed.
MSC:
 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
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References:
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