SpringerLink
Log in

Uniform nonintegrability of random variables

  • Research Article
  • Published:
Frontiers of Mathematics in China Aims and scope Submit manuscript

Abstract

Recently, T. K. Chandra, T. -C. Hu and A. Rosalsky [Statist. Probab. Lett., 2016, 116: 27–37] introduced the notion of a sequence of random variables being uniformly nonintegrable, and presented a list of interesting results on this uniform nonintegrability. We introduce a weaker definition on uniform nonintegrability (W-UNI) of random variables, present a necessary and sufficient condition for W-UNI, and give two equivalent characterizations of W-UNI, one of which is a W-UNI analogue of the celebrated de La Vallée Poussin criterion for uniform integrability. In addition, we give some remarks, one of which gives a negative answer to the open problem raised by Chandra et al.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chandra T K. De La Vallée Poussin’s theorem, uniform integrability, tightness and moments. Statist Probab Lett, 2015, 107: 136–141

    Article  MathSciNet  MATH  Google Scholar 

  2. Chandra T K, Hu T -C, Rosalsky A. On uniform nonintegrability for a sequence of random variables. Statist Probab Lett, 2016, 116: 27–37

    Article  MathSciNet  MATH  Google Scholar 

  3. Chong K M. On a theorem concerning uniform integrability. Publ Inst Math (Beograd) (NS), 1979, 25(39): 8–10

    MathSciNet  MATH  Google Scholar 

  4. Chow Y S, Teicher H. Probability Theory: Independence, Interchangeability, Martingales. 3rd ed. New York: Springer-Verlag, 1997

    Book  MATH  Google Scholar 

  5. Chung K L. A Course in Probability Theory. 2nd ed. New York: Academic Press, 1974

    MATH  Google Scholar 

  6. Hu T-C, Rosalsky A. A note on the de La Vallée Poussin criterion for uniform integrability. Statist Probab Lett, 2011, 81: 169–174

    Article  MathSciNet  MATH  Google Scholar 

  7. Hu T-C, Rosalsky A. A note on random variables with an infinite absolute first moment. Statist Probab Lett, 2015, 97: 212–215

    Article  MathSciNet  MATH  Google Scholar 

  8. Klenke A. Probability Theory: A Comprehensive Course. 2nd ed. London: Springer-Verlag, 2014

    Book  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11371191).

Author information

Authors and Affiliations

  1. College of Mathematics, Sichuan University, Chengdu, 610064, China

    Zechun Hu & Xue Peng

Authors
  1. Zechun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xue Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xue Peng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, Z., Peng, X. Uniform nonintegrability of random variables. Front. Math. China 13, 41–53 (2018). https://doi.org/10.1007/s11464-017-0623-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11464-017-0623-6

Keywords

MSC

Search

Navigation