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MR821760 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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