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Journal of the London Mathematical Society 1983 s2-27(1):185-192; doi:10.1112/jlms/s2-27.1.185
© 1983 by London Mathematical Society
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© Oxford University Press

Matrix Transformations of Weakly Dependent Random Variables

Ferenc Móricz

Szeged University, Bolyai Institute Aradi vértanak tere 1, 6720 Szeged, Hungary

Let X0, X1... be random variables satisfying the inequality Formula for every sequence c0, c1,..., of coefficients and for every n = 0, 1,..., where 1 < p ≤ 2, r > p and C > 0 are constants. By the aid of a summability matrix T = {ank:n, k = 0, 1,...} we form the means Formula for n = 0, 1, .... We prove that Tn -> 0 almost surely as n -> {infty} under fairly general conditions on {ank}. Our result contains as special cases an earlier result of D. Borwein and another result stating a strong law of large numbers for the random variables Xk.


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