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A Glivenko-Cantelli theorem for empirical measures of independent but non-identically distributed random variables. (English) Zbl 0458.60023


MSC:

60F15 Strong limit theorems
60B10 Convergence of probability measures
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References:

[1] Dudley, R. M., Convergence of Baire measures, Studia Math., 27, 251-268 (1966) · Zbl 0147.31301
[2] Dudley, R. M., Distances of probability measures and random variables, Ann. Math. Statist., 39, 1563-1572 (1968) · Zbl 0169.20602
[3] Dudley, R. M., The speed of mean Glivenko-Cantelli convergence, Ann. Math. Statist., 40, 40-50 (1969) · Zbl 0184.41401
[4] Dudley, R. M., Probabilities and metrics; Convergence of laws on metric spaces with a view to statistical testing, (Lecture Notes Series No. 45 (1976), Mathematics Institute, Aarhus University: Mathematics Institute, Aarhus University Aarhus, Denmark) · Zbl 0355.60004
[5] Fortet, R.; Mourier, E., Convergence de la répartition empirique vers la répartition théorique, Ann. Sci. École Norm. Sup., 70, 266-285 (1953) · Zbl 0053.09601
[6] LeCam, L., Convergence in distribution of stochastic processes, Univ. of Calif. Publications in Statistics, 2, 11, 207-236 (1957)
[7] Shorack, G. R., The weighted empirical process of row independent random variables with arbitrary d.f.’s, Statistica Neerlandica, 33, 169-189 (1979) · Zbl 0436.60009
[8] Varadarajan, V. S., On the convergence of sample probability distributions, Sankhyā, 19, 23-26 (1958) · Zbl 0082.34201
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