Abstract

Let {~, ~, P} be a probability space. We consider the series ~=~ ~ (~)/,, (x), (i) where ~ ~ f~, M ~ = O, M ~ m ----r,~,.; /~ (x) , oo ~ x ~ oo, a re f u n c t i o n s such t h a t f n ( z ) , r e g a r d ed as functions of a complex variable, are entire transcendental functions of exponential type with index Xn, for which sup [fn (x) I ---A, < oo. Following [i], we shall say that/,~(g) Bx. We assume that %~ § ~ as n § = and kk<%m for k<m. Let

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