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Literature Cited
R. M. Dudley, “Weak convergence of probabilities on non-separable metric spaces and empirical measures on euclidean spaces,” Illinois J. Math.,10, No. 4, 109–126 (1966).
M. Osörgö and P. Revesz, “A new method to prove Strassen type laws of invariance principle, II,” Z. Wahrscheinlichkeitstheorie Verw. Geb.,31, No. 4, 261–269 (1975).
J. Komlos, P. Major, and G. Tusnady, “An approximation of partial sums of independent RV-s and the sample DF. I,” Z. Wahrscheinlichkeitstheorie Verw. Geb.,32, Nos. 1–2, 111–133 (1975).
G. Tusnady, “A remark on the approximation of the sample DF in the multidimensional case,” Period. Math. Hung.,8, No. 1, 53–55 (1977).
I. S. Borisov, “On the sharpness of approximation of empirical fields,” Teor. Veroyat. Ee Primen.,26, No. 3, 646–647 (1981).
W. Philipp and L. Pinzur, “Almost sure approximation theorems for the multivariate empirical processes,” Z. Wahrscheinlichkeitstheorie Verw. Geb.,54, No. 1, 1–13 (1980).
V. V. Yurinskii, “On the inequalities for large deviations of certain statistics,” Teor. Veroyat. Ee Primen.,16, No. 2, 386–389 (1971).
V. V. Petrov, Sums of Independent Random Variables, Springer-Verlag (1975).
A. A. Borovkov, A Course of Probability Theory [in Russian], Nauka, Moscow (1972).
V. V. Yurinskii, “Exponential estimates for sums of independent random vectors,” Doctoral Dissertation, Moscow (1973).
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Mathematics Institute, Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 23, No. 5, pp. 31–41, September–October, 1982.
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Borisov, I.S. Approximation of empirical fields, constructed with respect to vector observations with dependent components. Sib Math J 23, 615–623 (1982). https://doi.org/10.1007/BF00971279
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DOI: https://doi.org/10.1007/BF00971279