Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Geometrical and Statistical Aspects of Probability in Banach Spaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1193))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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. 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. Kanter, M.: Probability inequalities for convex sets. J. Multivariate Anal. 6, 222–236 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  4. 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).

    Article  MathSciNet  MATH  Google Scholar 

  5. Ledoux, M.: The law of the iterated logarithm in uniformly convex Banach spaces. Trans. Amer. Math. Soc. (May 1986).

    Google Scholar 

  6. Pisier, G.: Martingales with values in uniformly convex spaces. Israel J. Math. 20, 326–350 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  7. 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).

    MATH  Google Scholar 

  8. 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).

    Article  MathSciNet  MATH  Google Scholar 

  9. Talagrand, M.: The Glivenko-Cantelli problem. Annals of Math., to appear (1984).

    Google Scholar 

  10. Yurinskii, V.V.: Exponential bounds for large deviations. Theor. Probability Appl. 19, 154–155 (1974).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématique, Université Louis-Pasteur, 7, rue René-Descartes, F-67084, Strasbourg, France

    Michel Ledoux

Authors
  1. Michel Ledoux
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Xavier Fernique Bernard Heinkel Paul-André Meyer Michael B. Marcus

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Ledoux, M. (1986). On the small balls condition in the central limit theorem in uniformly convex spaces. In: Fernique, X., Heinkel, B., Meyer, PA., Marcus, M.B. (eds) Geometrical and Statistical Aspects of Probability in Banach Spaces. Lecture Notes in Mathematics, vol 1193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077099

Download citation

  • DOI: https://doi.org/10.1007/BFb0077099

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16487-6

  • Online ISBN: 978-3-540-39826-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation