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MR821760 (87k:60086) 60F10 (60F05)
Pinelis, I. F. Asymptotic equivalence of the probabilities of large deviations for sums and maximum of independent random variables. (Russian) Limit theorems of probability theory, 144--173, 176, Trudy Inst. Mat., 5, ``Nauka'' Sibirsk. Otdel., Novosibirsk, 1985.
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