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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:
[1] LOEVE M.: Probability Theory (3rd. Van Nostrand, London, 1963. · Zbl 0108.14202
[2] POTOCKÝ R.: A strong law of large numbers for identically distributed vector lattice-valued random variables. Math. Slovaca 34 (1984), 67-72. · Zbl 0599.60038
[3] QI Y.: Limit theorems for sums and maxima of pairwise negative quadrant dependent random variables. Systems Sci. Math. Sci. 8 (1995), 249-253. · Zbl 0841.60020
[4] RENYI A.: Probability Theory. Academia, Prague, 1972. · Zbl 0265.01004
[5] WANG X. C.-BHASKARA RAO M.: A note on convergence of weighted sums of random variables. J. Multivariate Anal. 15 (1984), 124-134. · Zbl 0546.60006
[6] URBANÍKOVÁ M.: Limit theorems for B-lattice valued random variables. Math. Slovaca 52 (2002), 99-108. · Zbl 1007.60002
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