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(iv For every array of independent mean zero random elements, for every array of positive real numbers satisfying (1.5) and as, the condition (2.14) implies (1.2).
But for every array of positive real numbers, is a martingale difference array such that (2.31).
(iii For every array of integrable independent mean zero random elements, for every array of positive real numbers satisfying (1.5), for any, and for any points, there exists a positive constant such that (2.13) holds.
(ii For every array of integrable independent mean zero random elements, there exists a positive constant such that (2.12) holds.
(iv For every martingale difference array, for every array of positive real numbers satisfying (1.5) and as, the condition (2.14).
Remark 2.4 ensures that the inequality (2.15) holds for every and for every array of independent mean zero random elements in a real separable Banach space.
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