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References
G. J. Babu, On the mean values and distributions of arithmetical functions,Acta Arithm.,40, 63–77 (1981).
G. J. Babu, Distribution of the values of ω in short intervals,Acta Math. Acad. Sci. Hung.,40, 135–137 (1982).
G. J. Babu and P. Erdös, A note on the distribution function of additive arithmetical functions in short intervals,Canad. Math. Bull.,32, 441–445 (1989).
P. J. Billingsley,Convergence of Probability Measures, Wiley, New York (1968).
P. D. T. A. Elliott,Probabilistic Number Theory, Vol. 1, Springer-Verlag, Berlin (1979).
P. D. T. A. Elliott, Localised value-distribution of additive arithmetic functions,J. Reine Angew. Math.,379, 64–75 (1987).
P. D. T. A. Elliott, Additive arithmetic functions on intervals,Math. Proc. Cambr. Phil. Soc.,103, 163–179 (1988).
B. Grigelionis and R. Mikulevičius, On functional limit theorems of probabilistic number theory,Liet. Matem. Rink.,24, 72–81 (1984).
A. Hildebrand, Multiplicative functions in short intervals,Canad. J. Math.,39, 646–672 (1987).
K.-H. Indlekofer,Limiting distributions of additive functions in short intervals, to appearin Acta Math. Acad. Sci. Hung., preprint (1986).
K.-H. Indlekofer,Limit laws and moments of additive functions in short intervals, preprint (1986).
Z. Kryžius, Distribution of additive arithmetic functions with shifted arguments,Liet. Matem. Rink.,27, 100–112 (1987).
J. Kubilius,Probabilistic Methods in the Theory of Numbers, Transl. Math. Monographs, vol. 11, Amer. Math. Soc., Providence, RI (1964).
E. Manstavičius, On arithmetic modelling of random processes,Liet. Matem. Rink.,24, 148–161 (1984).
E. Manstavičius, Additive functions and random processes,Liet. Matem. Rink.,25, 97–109 (1985).
E. Manstavičius, An invariance principle for additive arithmetic functions,Dokl. Acad. Sci. USSR,298, 1316–1320 (1988).
N. V. Neustroev, Distribution of values of additive functions in short intervals, preprint of the Inst. of Sci. Techn. Information of the USSR 3883-84 (1984).
N. M. Timofeev and H. H. Usmanov, On the arithmetic modelling of the Brownian motion,Dokl. Acad. Sci. TadzhSSR,25, 207–211 (1982).
N. M. Timofeev and H. H. Usmanov, On the arithmetic modelling of random processes with independent increments,Dokl. Acad. Sci. TadzhSSR,275, 556–559 (1984).
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Translated from Lietuvos Matematikos Rinkinys, Vol. 33, No. 3, pp. 280–292, July–September, 1993
Translated by E. Manstavičius
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Indlekofer, K.H., Manstavičius, E. Functional limit theorems for additive arithmetic functions on intervals. Lith Math J 33, 217–226 (1993). https://doi.org/10.1007/BF00970938
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DOI: https://doi.org/10.1007/BF00970938