Metric entropy and the central limit theorem in C ( S )

R. M. Dudley

Annales de l'institut Fourier (1974)

  • Volume: 24, Issue: 2, page 49-60
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Dudley, R. M.. "Metric entropy and the central limit theorem in $C(S)$." Annales de l'institut Fourier 24.2 (1974): 49-60. <http://eudml.org/doc/74176>.

@article{Dudley1974,
abstract = {Central limit theorems with hypotheses in terms of $\varepsilon $-entropy are proved first in $C(S)$ where $S$ is a compact metric space and then in an arbitrary separable Banach space.},
author = {Dudley, R. M.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {49-60},
publisher = {Association des Annales de l'Institut Fourier},
title = {Metric entropy and the central limit theorem in $C(S)$},
url = {http://eudml.org/doc/74176},
volume = {24},
year = {1974},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 2
SP - 49
EP - 60
AB - Central limit theorems with hypotheses in terms of $\varepsilon $-entropy are proved first in $C(S)$ where $S$ is a compact metric space and then in an arbitrary separable Banach space.
LA - eng
UR - http://eudml.org/doc/74176
ER -

References

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  1. Aloisio de ARAUJO, On the central limit theorem for C(Ik) valued random variables (preprint, Statistics Dept., Univ. of Calif., Berkeley), 1973. 
  2. G. BENNETT, Probability inequalities for the sum of independent random variables, Jour. Amer. Statist. Assoc., 57 (1962), 33-45. Zbl0104.11905
  3. R. M. DUDLEY, Sample functions of the Gaussian process, Ann. Probability, 1 (1973), 66-103. Zbl0261.60033MR49 #11605
  4. R. FORTET and E. MOURIER, Les fonctions aléatoires comme éléments aléatoires dans les espaces de Banach, Studia Math., 15 (1955), 62-79. Zbl0068.11104MR19,1202b
  5. Evarist GINÉ, On the central limit theorem for sample continuous processes, to appear in Annals of Probability, 1974. Zbl0288.60017
  6. Evarist GINÉ, A note on the central limit theorem in C(S), (preprint), 1973. 
  7. M. LOÈVE, (1963), Probability Theory (Princeton, Van Nostrand). Zbl0108.14202MR34 #3596
  8. V. STRASSEN and R. DUDLEY, (1969), The central limit theorem and ε-en-tropy, Lecture Notes in Math., 89, 224-231. Zbl0196.21101MR43 #5593

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