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The Brunk-Prokhorov strong law of large numbers for fields of martingale differences taking values in a Banach space. (English) Zbl 1281.60030
Summary: We define a new type of fields of martingale differences taking values in Banach spaces and establish the Brunk-Prokhorov strong laws of large numbers and the convergence rate in the strong laws of large numbers for such fields.

MSC:
60F15 Strong limit theorems
60B11 Probability theory on linear topological spaces
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
60F25 \(L^p\)-limit theorems
60G42 Martingales with discrete parameter
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