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1. CMB 2004 (vol 47 pp. 475)

 Uniqueness of Almost Everywhere Convergent Vilenkin Series D. J. Grubb [3] has shown that uniqueness holds, under a mild growth condition, for Vilenkin series which converge almost everywhere to zero. We show that, under even less restrictive growth conditions, one can replace the limit function 0 by an arbitrary $f\in L^q$, when $q>1$. Categories:43A75, 42C10