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# Uniqueness of Almost Everywhere Convergent Vilenkin Series

Published:2004-09-01
Printed: Sep 2004
• W. R. Wade
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## Abstract

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 $q>1$.
 MSC Classifications: 43A75 - Analysis on specific compact groups 42C10 - Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

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