Summary
In this paper, we discuss the rate of convergence in the mean central limit theorem for weakly multiplicative systems and apply this result to lacunary trigonometric series under probability measures on ℝ with Hölder continuous distribution function.
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Fukuyama, K. A mean central limit theorem for weakly multiplicative systems and its application to lacunary trigonometric series. Probab. Th. Rel. Fields 89, 159–179 (1991). https://doi.org/10.1007/BF01366904
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DOI: https://doi.org/10.1007/BF01366904