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The law of the iterated logarithm in \(C[0,1]\). (English) Zbl 0299.60019


MSC:

60F05 Central limit and other weak theorems
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[1] Dudley, R. M., The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Functional Analysis, 1, 290-330 (1967) · Zbl 0188.20502
[2] Dudley, R. M.; Strassen, V., The central limit theorem and ε-entropy, Lecture Notes in Math. 89, 224-231 (1969), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York · Zbl 0196.21101
[3] Dudley, R. M., Metric entropy and the central limit theorem in C(S), Ann. Inst. Fourier, 24, 49-60 (1974) · Zbl 0275.60033
[4] Giné, E., On the central limit theorem for sample continuous processes, Ann. Probability, 2, 629-641 (1974) · Zbl 0288.60017
[5] Hartman, P.; Wintner, A., On the law of the interated logarithm, Amer. J. Math., 63, 169-176 (1941) · JFM 67.0460.03
[6] Jain, N.C., Marcus, Michael B.: Central limit theorems for C(S) valued random variables (preprint) · Zbl 0305.60004
[7] Kuelbs, J., An inequality for the distribution of a sum of certain Banach space valued random variables, Studia Math., 52, 69-87 (1974) · Zbl 0306.60004
[8] Kuelbs, J.: A strong convergence theorem for Banach space valued random variables. (Submitted for publication) · Zbl 0365.60034
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