Central limit theorems with hypotheses in terms of -entropy are proved first in where is a compact metric space and then in an arbitrary separable Banach space.
On démontre un théorème limite central, en utilisant l’-entropie, d’abord dans où est un compact métrisable, puis dans un espace de Banach séparable quelconque.
@article{AIF_1974__24_2_49_0, author = {Dudley, R. M.}, 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}, number = {2}, year = {1974}, doi = {10.5802/aif.505}, mrnumber = {54 #3807}, zbl = {0275.60033}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.505/} }
TY - JOUR AU - Dudley, R. M. TI - Metric entropy and the central limit theorem in $C(S)$ JO - Annales de l'Institut Fourier PY - 1974 SP - 49 EP - 60 VL - 24 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.505/ DO - 10.5802/aif.505 LA - en ID - AIF_1974__24_2_49_0 ER -
Dudley, R. M. Metric entropy and the central limit theorem in $C(S)$. Annales de l'Institut Fourier, Volume 24 (1974) no. 2, pp. 49-60. doi : 10.5802/aif.505. http://archive.numdam.org/articles/10.5802/aif.505/
On the central limit theorem for C(Ik) valued random variables (preprint, Statistics Dept., Univ. of Calif., Berkeley), 1973.
,Probability inequalities for the sum of independent random variables, Jour. Amer. Statist. Assoc., 57 (1962), 33-45. | Zbl
,Sample functions of the Gaussian process, Ann. Probability, 1 (1973), 66-103. | MR | Zbl
,Les fonctions aléatoires comme éléments aléatoires dans les espaces de Banach, Studia Math., 15 (1955), 62-79. | MR | Zbl
and ,On the central limit theorem for sample continuous processes, to appear in Annals of Probability, 1974. | Zbl
,A note on the central limit theorem in C(S), (preprint), 1973.
,Probability Theory (Princeton, Van Nostrand). | MR | Zbl
, (1963),The central limit theorem and ε-en-tropy, Lecture Notes in Math., 89, 224-231. | MR | Zbl
and , (1969),Cited by Sources: