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Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability. (English) Zbl 1065.60022
A new concept of integrability, called \(h\)-integrability, is introduced and, under this condition, mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables are obtained.

MSC:
60F05 Central limit and other weak theorems
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
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