Advertisement

On the small balls condition in the central limit theorem in uniformly convex spaces

  • Michel Ledoux
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1193)

Keywords

Banach Space Central Limit Theorem Convex Space Iterate Logarithm Convex Banach Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [A-A-G]
    de Acosta, A., Araujo, A., Giné, E.: On Poisson measures, Gaussian measures, and the central limit theorem in Banach spaces. Advances in Prob., vol. 4, 1–68, Dekker, New York (1978).Google Scholar
  2. [H-J]
    Hoffmann-Jørgensen, J.: On the modulus of smoothness and the G±-conditions in B-spaces. Aarhus Preprint Series 1974–75, no2 (1975).Google Scholar
  3. [K]
    Kanter, M.: Probability inequalities for convex sets. J. Multivariate Anal. 6, 222–236 (1978).MathSciNetCrossRefzbMATHGoogle Scholar
  4. [L1]
    Ledoux, M.: Sur une inégalité de H.P. Rosenthal et le théorème limite central dans les espaces de Banach. Israel J. Math. 50, 290–318 (1985).MathSciNetCrossRefzbMATHGoogle Scholar
  5. [L2]
    Ledoux, M.: The law of the iterated logarithm in uniformly convex Banach spaces. Trans. Amer. Math. Soc. (May 1986).Google Scholar
  6. [P1]
    Pisier, G.: Martingales with values in uniformly convex spaces. Israel J. Math. 20, 326–350 (1975).MathSciNetCrossRefzbMATHGoogle Scholar
  7. [P2]
    Pisier, G.: Le théorème de la limite centrale et la loi du logarithme itéré dans les espaces de Banach. Séminaire Maurey-Schwartz 1975–76, exposés 3 et 4, Ecole Polytechnique, Paris (1976).zbMATHGoogle Scholar
  8. [P-Z]
    Pisier, G., Zinn, J.: On the limit theorems for random variables with values in the spaces Lp (2 ≤ p < ∞). Zeit. für Wahr. 41, 289–304 (1978).MathSciNetCrossRefzbMATHGoogle Scholar
  9. [T]
    Talagrand, M.: The Glivenko-Cantelli problem. Annals of Math., to appear (1984).Google Scholar
  10. [Y]
    Yurinskii, V.V.: Exponential bounds for large deviations. Theor. Probability Appl. 19, 154–155 (1974).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Michel Ledoux
    • 1
  1. 1.Département de MathématiqueUniversité Louis-PasteurStrasbourgFrance

Personalised recommendations