Study of almost everywhere convergence of series by means of martingale methods
Abstract
Martingale methods are used to study the almost everywhere convergence of general function series. Applications are given to ergodic series, which improves recent results of Fan FanETDS, and to dilated series, including Davenport series, which completes results of Gaposhkin Gaposhkin67 (see also Gaposhkin68). Application is also given to the almost everywhere convergence with respect to Riesz products of lacunary series.
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