Abstract
Random measures of the form are considered, where is a unit mass concentrated at the point . For any sequence of natural numbers it is established that for almost all sequences the partial sums of the Fourier-Stieltjes series of the measure have order for almost all . As proved by Kahane in 1961, the order cannot be improved. This result is connected with the well-known problem of Zygmund of finding the exact order of growth of the partial sums of Fourier series almost everywhere. Bibliography: 15 titles.
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