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The sequence {Xn} is said to be multiplicative if the expectation E(XiχXi2 Xιn) — 0 whenever 0 < iλ < i2 < •••</„; in particular, it is multiplicative if it is independent with EXn — 0 for n — 0,1, Condition (2) is trivially satisfied when {Xn} is multiplicative. The nature of Theorem A is clarified by comparison with Kolmogorov's classical strong law of large numbers which states that if {Xn} is independent with EXn = 0 for n = 0 ,1 , . . . , and if

Transformations of certain sequences of random variables by generalized Hausdorff matrices