摘要

Let {X,X (n) ; n a parts per thousand yen 0} be a sequence of independent and identically distributed random variables, taking values in a separable Banach space (B,aEuro- center dot aEuro-) with topological dual B*. Considering the geometrically weighted series for 0 < beta < 1, and a sequence of positive constants {h(n), n a parts per thousand yen 1}, which is monotonically approaching infinity and not asymptotically equivalent to log log n, a limit result for is achieved.