Skip to main content

On uniform convergence of measures with applications to uniform convergence of empirical distributions

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 566))

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cantelli, F.P. (1933). Sulla determinazione empirica delle leggi die probabilita. Ist. Ital. Attnari 4, 421–424.

    MATH  Google Scholar 

  2. Dehardt, J. (1971). Generalizations of the Glivenko-Cantelli theorem. Ann. Math. Statist. 42, 2050–2055.

    Article  MathSciNet  MATH  Google Scholar 

  3. Elker, J. (1975). Über ein gleichmäßiges Gesetz der großen Zahlen. Diplomarbeit. Ruhr-Universität Bochum.

    Google Scholar 

  4. Fabian, V. (1970). On uniform convergence of measures. Z. Wahrscheinlichkeitstheorie verw. Gebiete 15, 139–143.

    Article  MathSciNet  Google Scholar 

  5. Gaenssler, P. (1973). On convergence of sample distributions. Bull. Internat. Statist. Inst. 45,1, 427–432.

    MathSciNet  Google Scholar 

  6. Gaenssler, P. (1974). Around the Glivenko-Cantelli theorem. In: Limit theorems of Probability Theory; Keszthely. Ed. by P. Révész, 93–103.

    Google Scholar 

  7. Gaenssler, P. and Stute, W. (1975/76). A survey on some results for empirical processes in the i.i.d. case. RUB-Preprint Series No. 15.

    Google Scholar 

  8. Glivenko, V. (1933). Sulla determinazione empirica della legge die probabilita. Giorn. Ist. Ital. Attnari 4, 92–99.

    MATH  Google Scholar 

  9. Halmos, P. (1958). Measure Theory. Princeton: Van Nostrand.

    MATH  Google Scholar 

  10. Kiefer, J. (1961). On large deviations of the empiric D.F. of vector chance variables and a law of iterated logarithm. Pacif. J. Math. 11, 649–660.

    Article  MathSciNet  MATH  Google Scholar 

  11. Krickeberg, K. (1976). An alternative approach to Glivenko-Cantelli theorems. In this volume.

    Google Scholar 

  12. Rao, R.R. (1962). Relations between weak and uniform convergence of measures with appl.. Ann. Math. Statist. 33, 659–680.

    Article  MathSciNet  MATH  Google Scholar 

  13. Stute, W. (1976). On a generalization of the Glivenko-Cantelli theorem. Z. Wahrscheinlichkeitstheorie verw. Gebiete 35, 167–175.

    Article  MathSciNet  MATH  Google Scholar 

  14. Stute, W. (1974). On uniformity classes of functions with an application to the speed of mean Glivenko-Cantelli convergence. RUB-Preprint Series No. 5.

    Google Scholar 

  15. Stute, W. (1975). Convergence rates for the isotrope discrepancy. To appear in Ann. Probability.

    Google Scholar 

  16. Topsøe, F. (1970). Topology and Measure. Lecture Notes in Mathematics 133. Berlin: Springer.

    MATH  Google Scholar 

  17. Topsøe, F., Dudley, R.M. and Hoffmann-Jørgensen, J. (1976). Two examples concerning uniform convergence of measures w.r.t. balls in Banach spaces. In this volume.

    Google Scholar 

  18. Topsøe, F. (1976). Uniformity in convergence of measures. Preprint Series No. 27. University of Copenhagen.

    Google Scholar 

  19. Valentine, F. (1968). Konvexe Mengen. Mannheim: Bibliographisches Institut. Band 402/402 a.

    MATH  Google Scholar 

  20. Wolfowitz, J. (1954). Generalizations of the theorem of Glivenko-Cantelli. Ann. Math. Statist. 25, 131–138.

    Article  MathSciNet  MATH  Google Scholar 

  21. Wolfowitz, J. (1960). Convergence of the empiric distribution function on half-spaces. Contrib. to Probability and Statist., 504–507.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Peter Gaenssler Pál Révész

Rights and permissions

Reprints and permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Gaenssler, P., Stute, W. (1976). On uniform convergence of measures with applications to uniform convergence of empirical distributions. In: Gaenssler, P., Révész, P. (eds) Empirical Distributions and Processes. Lecture Notes in Mathematics, vol 566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096878

Download citation

  • DOI: https://doi.org/10.1007/BFb0096878

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08061-9

  • Online ISBN: 978-3-540-37515-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics