A mean convergence theorem and weak law for arrays of random elements in martingale type \(p\) Banach spaces

DOI10.1016/S0167-7152(97)85593-9zbMath0874.60008OpenAlexW2078651144MaRDI QIDQ1359781

Andrew Rosalsky, André Adler, Andrei I. Volodin

Publication date: 6 July 1997

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(97)85593-9

zbMATH Keywords

weak law of large numbersweighted sumsconvergence in probabilityuniformly integrableCesàro uniformly integrable arrayreal separable martingale type \(p\) Banach space

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Probability theory on linear topological spaces (60B11) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12) (L^p)-limit theorems (60F25)

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Cites Work

• Geometry and probability in Banach spaces. Notes by Paul R. Chernoff
• The weak law of large numbers for arrays
• Martingales with values in uniformly convex spaces
• The law of large numbers and the central limit theorem in Banach spaces
• On the weak law of large numbers for arrays
• Convergence of weighted sums of random variables and uniform integrability concerning the weights
• Abstract martingale convergence theorems
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