Metric entropy and the central limit theorem in C(S)
Annales de l'Institut Fourier, Tome 24 (1974) no. 2, pp. 49-60.

On démontre un théorème limite central, en utilisant l’ε-entropie, d’abord dans C(S) où S est un compact métrisable, puis dans un espace de Banach séparable quelconque.

Central limit theorems with hypotheses in terms of ε-entropy are proved first in C(S) where S is a compact metric space and then in an arbitrary separable Banach space.

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     title = {Metric entropy and the central limit theorem in $C(S)$},
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Dudley, R. M. Metric entropy and the central limit theorem in $C(S)$. Annales de l'Institut Fourier, Tome 24 (1974) no. 2, pp. 49-60. doi : 10.5802/aif.505. http://www.numdam.org/articles/10.5802/aif.505/

Aloisio De Araujo, On the central limit theorem for C(Ik) valued random variables (preprint, Statistics Dept., Univ. of Calif., Berkeley), 1973.

G. Bennett, Probability inequalities for the sum of independent random variables, Jour. Amer. Statist. Assoc., 57 (1962), 33-45. | Zbl

R. M. Dudley, Sample functions of the Gaussian process, Ann. Probability, 1 (1973), 66-103. | MR | Zbl

R. Fortet and E. Mourier, Les fonctions aléatoires comme éléments aléatoires dans les espaces de Banach, Studia Math., 15 (1955), 62-79. | MR | Zbl

Evarist Giné, On the central limit theorem for sample continuous processes, to appear in Annals of Probability, 1974. | Zbl

Evarist Giné, A note on the central limit theorem in C(S), (preprint), 1973.

M. Loève, (1963), Probability Theory (Princeton, Van Nostrand). | MR | Zbl

V. Strassen and R. Dudley, (1969), The central limit theorem and ε-en-tropy, Lecture Notes in Math., 89, 224-231. | MR | Zbl

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