Skip to main content
Log in

The Glivenko-Cantelli problem, ten years later

  • Published:
Journal of Theoretical Probability Aims and scope Submit manuscript

Abstract

We give simple proofs of previous characterizations of Glivenko-Cantelli classes.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dudley, R. M. (1984). A course on empirical processes,Lecture Notes in Math., Springer-Verlag,1067, 2–142.

    Google Scholar 

  2. Elton, J. (1983). Sign embedding of nl ,Trans. Am. Math. Soc. 279, 113–124.

    Google Scholar 

  3. Fremlin, D. Private communication.

  4. Giné, E., and Zinn, J. (1984). Some limit theorems for empirical processes,Ann. Prob. 2, 929–983.

    Google Scholar 

  5. Hoffman-Jørgensen, J. (1985). The law of large numbers for nonmeasurable and nonseparable random elements, Colloque en l'honneur de L. Schwartz,Astérisque, Herman, Paris131, 299–356.

    Google Scholar 

  6. Ledoux, M., and Talagrand, M. (1991).Probability in Banach spaces, Springer-Verlag.

  7. Sauer, N. (1972). On the density of families of sets,J. Comb. Theor. 13, 145–147.

    Google Scholar 

  8. Shelah, S. (1972). A combinatorial problem: stability and order for models and theories in infinitary languages.Pacific J. Math. 41, 274–261.

    Google Scholar 

  9. Talagrand, M. (1984). Pettis integral and measure theory,Mem. Am. Math. Soc., Vol. 307.

  10. Talagrand, M. (1987). The Glivenko-Cantelli problem.Ann. Prob. 6, 837–870.

    Google Scholar 

  11. Talagrand, M. (1988). Donsker classes of sets,Prob. Th. Rel. Fields 78, 169–191.

    Google Scholar 

  12. Talagrand, M. (1993). Regularity of infinitely divisible processes,Ann. Prob. 21, 362–432.

    Google Scholar 

  13. Vapnik, V. N., and Čhervonenkis, A. Y. (1971). On the uniform convergence of relative frequencies of events to their probabilities.Th. Prob. Appl. 16, 264–280.

    Google Scholar 

  14. Vapnik, V. N., and Čhervonenkis, A. Y. (1981). Necessary and sufficient conditions for the uniform convergence of means to their expectations,Th. Prob. Appl. 26, 532–553.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Work partially supported by an NSF grant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Talagrand, M. The Glivenko-Cantelli problem, ten years later. J Theor Probab 9, 371–384 (1996). https://doi.org/10.1007/BF02214655

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02214655

Key Words

Navigation