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Literature cited
V. Strassen, “An invariance principle for the law of the iterated logarithm,” Z. Wahrschein. Verw. Gebiete,3, No. 3, 221–226 (1964).
W. Philipp and F. Stout, “Almost-sure invariance principles for partial sums of weakly dependent random variables,” Mem. Am. Math. Soc.,2, No. 161, 1–140 (1975).
I. Berkes and W. Philipp, “Approximation theorems for independent and weakly dependent random vectors,” Ann. Probab.,7, No. 1, 29–54 (1979).
I. Berkes and G. Morrow, “Strong invariance principles for the mixing random fields,” Z. Wahrschein. Verw. Gebiete,57, No. 1, 15–37 (1981).
G. Morrow, “Approximation of rectangular sums of B-valued random variables,” Z. Wahrschein. Verw. Gebiete,57, No. 2, 265–291 (1981).
B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley (1968).
A. Gut, “Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices,” Ann. Probab.,8, No. 2, 298–313 (1980).
A. V. Bulinskii, “A new version of the functional law of the iterated logarithm,” Teor. Veroyatn. Primen.,25, No. 3, 502–512 (1980).
N. M. Zinchenko, “On the functional law of the iterated logarithm for multiparameter Brownian motion,” Teor. Veroyatn. Mat. Statistika, No. 29, 46–51 (1983).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 36, No. 2, pp. 149–154, March–April, 1984.
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Zinchenko, N.M. Approximation of sums of random variables with multiindexes. Ukr Math J 36, 133–138 (1984). https://doi.org/10.1007/BF01066943
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DOI: https://doi.org/10.1007/BF01066943