Abstract
Central limit theorems are obtained for martingale arrays without the requirement of uniform asymptotic negligibility. The results obtained generalise the sufficiency part of Zolotarev's extension of the classical Lindeberg-Feller central limit theorem [V.M. Zolotarev, Theor. Probability Appl. 12 (1967), 608–618] and also the main martingale central limit theorem (not functional central limit theorem however) of D.L. McLeish [Ann. Probability 2 (1974), 620–628.
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