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Mesures majorantes et théorème de la limite centrale dans C(S). (French) Zbl 0336.60021


MSC:

60F05 Central limit and other weak theorems
60B05 Probability measures on topological spaces
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[1] Billingsley, P., Convergence of probability measures (1968), New-York: Wiley, New-York · Zbl 0172.21201
[2] 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
[3] Dudley, R. M., Metric entropy and the central limit theorem in C(S), Ann. Inst. Fourier, 24, 2, 49-60 (1974) · Zbl 0275.60033
[4] Fernique, X.: Régularité des trajectoires des fonctions aléatoires gaussiennes. Ecole d’Eté de Probabilités de St Flour 4 (1974); Lecture Notes in Math. 480, 1-96, Berlin-Heidelberg-New York: Springer 1974 · Zbl 0331.60025
[5] Garsia, A. M.; Rodemich, E.; Rumsey, H. Jr., A real variable lemma and the continuity of some gaussian processes, Indiana Univ. Maths J., 20, nℴ 6, 565-578 (1970) · Zbl 0252.60020
[6] Giné, E., On the central limit theorem for sample continuous processes, Ann. Probability, 2, 629-641 (1974) · Zbl 0288.60017
[7] Heinkel, B., Théorème central-limite et loi du logarithme itéré dans C(S), C.R. Acad. Sci. Paris, 282, 711-713 (1976) · Zbl 0331.60016
[8] Heinkel, B.: Théorème de dérivation du type de celui de Lebesgue et continuité p.s. des trajectoires de certains processus gaussiens (1974). Séminaire de Probabilités VIII; Lecture Notes in Math. 381, 155-171. Berlin-Heidelberg-New York: Springer · Zbl 0286.60019
[9] Jain, N. C.; Marcus, M. B., Central-limit theorems for C(S)-valued random variables, J. Functional Analysis, 19, 216-231 (1975) · Zbl 0305.60004
[10] Jain, N.C., Marcus, M.B.: Sufficient conditions for the continuity of stationary gaussian processes and applications · Zbl 0336.60041
[11] Pisier, G.: Type des espaces normés. Séminaire Maurey-Schwartz, 1973-74, exposé nℴ 3
[12] Preston, C., Continuity properties of some gaussian processes, Ann. Math. Statist., 43, 285-292 (1972) · Zbl 0268.60044
[13] Zinn, J.: A note on the central-limit theorem in Banach spaces. A paraÎtre · Zbl 0402.60009
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