This is a preview of subscription content, log in via an institution to check access.
Literature Cited
P. D. T. A. Elliott, Probabilisitc Number Theory. I. Mean-Value Theorems, Springer-Verlag, New York-Heidelberg-Berlin (1979).
I. Katai, “On the distribution of arithmetical functions,” Acta Math. Acad. Sci. Hung.,20, No. 1–2, 69–87 (1969).
E. M. Paul, “Density in the light of probability theory. III,” Sankhya, Series A,25, No. 3, 273–280 (1963).
I. Z. Ruzsa, “Generalized moments of additive functions,” J. Number Theory,18, 27–33 (1984).
É. Manstavichyus, “Arithmetic simulation of stochastic processes,” Liet. Mat. Rinkinys,24, No. 3, 148–161 (1984).
V. Nakutis, “Analog of Erdös' theorem in Hilbert space,” in: Twenty-fifth Conference of the Lithuanian Mathematical Society. Abstracts of Reports [in Russian], Vilnius (1984), pp. 203–204.
V. V. Buldygin, Convergence of Random Elements in Topological Spaces [in Russian], Naukova Dumka, Kiev (1980).
A. Araujo and E. Gine, The Central Limit Theorem for Real and Banach Valued Random Variables, Wiley, New York-Chichester-Brisbane-Toronto (1980).
E. Gine, V. Mandrekar, and J. Zinn, “On sums of independent random variables with values in Lp (2≦p<∞).” Lect. Notes Math.,709, 111–124 (1979).
N. C. Jain, “Central limit theorem in a Banach space,” Lect. Notes Math.,526, 113–130 (1976).
N. N. Vakhaniya, V. I. Tarieladze, and S. A. Chobanyan, Probabilistic Distributions in Banach Spaces [in Russian], Nauka, Moscow (1985).
G. H. Hardy, D. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press (1952).
M. I. Tulyaganova, “Multidimensional distribution for additive functions with unit normalization,” Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 2, 29–35 (1974).
R. Slesoraitene, “Application of the method of H. Cramer and G. Wald for multidimensional distribution of additive arithmetic functions,” Liet. Mat. Rinkinys,16, No. 2, 155–172 (1976).
H. Halberstam and K. F. Roth, Sequences, Vol. 1, Clarendon Press, Oxford (1966).
Additional information
V. Kapsukas Vilnius State University. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 26, No. 2, pp. 298–309, April–June, 1986.
Rights and permissions
About this article
Cite this article
Nakutis, V. Analogs of the Erdös-Wintner theorem in cartain Banach spaces. Lith Math J 26, 145–153 (1986). https://doi.org/10.1007/BF00966148
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00966148