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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.

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