Skip to main content
SpringerLink
Log in

Order law of large numbers of the Marcinkiewicz–Zygmund type

  • Published:
Ukrainian Mathematical Journal Aims and scope

The order law of large numbers of the Marcinkiewicz–Zygmund type is established for random variables on Banach lattices. Similar results are also obtained for the maximum scheme.

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

Access this article

Log in via an institution

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. J. Marcinkiewicz and A. Zygmund, “Sur les fonctions indépendantes,” Fund. Math., 29, 60–90 (1937).

    Google Scholar 

  2. M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, Berlin (1991).

    MATH  Google Scholar 

  3. I. K. Matsak and A. M. Plichko, “On the Marcinkiewicz–Zygmund law of large numbers in Banach lattices,” Ukr. Mat. Zh., 62, No. 4, 504–513 (2010); English translation: Ukr. Math. J., 62, No. 4, 575–587 (2010).

    Article  MATH  Google Scholar 

  4. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Springer, Berlin (1979).

    MATH  Google Scholar 

  5. L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  6. I. K. Matsak, “A remark on the order law of large numbers,” Theor. Imovir. Mat. Stat., Issue 72, 84–92 (2005); English translation: Theory Probab. Math. Statist., No. 72, 93–102 (2006).

  7. A.V. Bukhvalov, A. I. Veksler, and V. A. Geiler, “Normed lattices,” in: VINITI Series in Mathematical Analysis [in Russian], Issue 18, VINITI, Moscow (1980), pp. 125–184.

  8. W. Feller, An Introduction to Probability Theory and Its Applications. Vol. 2 [Russian translation], Mir, Moscow (1984).

    Google Scholar 

  9. I. K. Matsak and A. M. Plichko, “On the maxima of independent random elements in Banach functional lattices,” Theor. Imovir. Mat. Stat., Issue 61, 105–116 (1999); English translation: Theory Probab. Math. Statist., No. 61, 109–120 (2000).

  10. J. A. Wellner, “A martingale inequality for the empirical process,” Ann. Probab., No. 2, 303–308 (1977).

    Google Scholar 

  11. N. N. Vakhaniya, V. I. Tarieladze, and S. A. Chobanyan, Probability Distributions in Banach Spaces [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  12. K. Yosida, Functional Analysis [Russian translation], Mir, Moscow (1967).

    Google Scholar 

  13. I. K. Matsak, “Evaluation of the moments of suprema of normalized sums of independent random variables,” Theor. Imovirn. Mat. Stat., Issue 67, 104–116 (2002); English translation: Theory Probab. Math. Statist., No. 67, 115–128 (2003).

  14. A.V. Skorokhod, Random Processes with Independent Increments [in Russian], Nauka, Moscow (1964).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv, Ukraine

    K. S. Akbash & I. K. Matsak

Authors
  1. K. S. Akbash
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. K. Matsak
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 12, pp. 1587–1597, December, 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Akbash, K.S., Matsak, I.K. Order law of large numbers of the Marcinkiewicz–Zygmund type. Ukr Math J 62, 1839–1851 (2011). https://doi.org/10.1007/s11253-011-0474-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-011-0474-3

Keywords

Search

Navigation