Literature cited
S. V. Nagaev, “Large deviations of sums of independent random variables,” Ann. Prob.,2, No. 5, 745–789 (1979).
A. D'Acosta and J. D. Samur, “Infinitely divisible probability measures,” Stud. Math.,46, No. 2, 143–160 (1979).
W. Feller, Introduction to Probability Theory and Its Applications, Vols. I and II, Wiley, New York (1968).
J.-P. Kahane, Random Series of Functions, Heath, Lexington (1968).
V. V. Buldygin, “On the Lévy inequality for random variables with values in a Banach space,” Teor. Veroyatn. Primen.,19, No. 1, 154–158 (1974).
V. V. Buldygin, Convergence of Random Elements in Topological Spaces [in Russian], Naukova Dumka, Kiev (1980).
H. P. Rosenthal, “On the subspaces of Lp (p>2) spanned by sequences of independent random variables,” Israel J. Math.,8, No. 3, 273–303 (1970).
E. Gine, V. Mandrekar, and J. Zinn, “On sums of independent random variables with values inL p (2≤p<∞), “ in: A. Beck (ed.), Probabilities in Banach Spaces. II, Lect. Notes in Math.,709, Springer-Verlag, Berlin-New York (1979), pp. 111–124.
I. F. Pinelis, “On the distribution of sums of independent random variables with values in a Banach space,” Teor. Veroyatn. Primen.,23, No. 2, 630–637 (1978).
A. D'Acosta, “Inequalities for B-value random vectors with applications to the strong law of large numbers,” Ann. Prob.,9, No. 1, 157–161 (1981).
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Translated from Matematicheskie Zametki, Vol. 34, No. 2, pp. 309–313, August, 1983.
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Nagaev, S.V. Probabilities of large deviations in Banach spaces. Mathematical Notes of the Academy of Sciences of the USSR 34, 638–640 (1983). https://doi.org/10.1007/BF01141784
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DOI: https://doi.org/10.1007/BF01141784