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Strong laws of large numbers for double sequences of random elements. (English) Zbl 0952.60013
A random element is a measurable transformation from a probability space to a Banach space \(B\). The measurability is considered with respect to the Borel subsets of \(B\) and expected value of a random element is defined to be the Pettis integral. Strong laws of large numbers are proved for double sequences of independent random elements. The results obtained are new even for real-valued random elements.
MSC:
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
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References:
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