Divergence of Random Power Series

then almost all series (1) diverge almost everywhere on I zl = 1 . Here almost all refers to the set of t (in the usual Lebesgue sense), while almost everywhere refers to the set of z on the circumference of the unit circle (again in the usual sense) . Only recently [1] was it observed that some nontrivial interesting assertions similar to the above with almost everywhere replaced by everywhere can be made . Here a new result of this kind, going beyond that indicated in [1], will be established .