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

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.

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.

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     title = {Metric entropy and the central limit theorem in $C(S)$},
     journal = {Annales de l'Institut Fourier},
     pages = {49--60},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {24},
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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

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

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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). | Zbl | MR

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

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