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This paper contains a general dependent extension of Doob's inequality for martingales, E (₈ ₍ Sᵢ²) 4ESₙ². This inequality is then used to extend the martingale convergence theorem for L₂ bounded variables, and to prove strong laws under dependent assumptions. Strong and -mixing variables are shown to satisfy the conditions of these theorems and hence strong laws are proved as well for these.
D. L. McLeish (Wed,) studied this question.