Skip to main content
SpringerLink
Log in

Weakly convergent sequences of Banach space valued random variables

  • Conference paper
  • First Online:
Banach Spaces of Analytic Functions

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 604))

Abstract

Examples are constructed of sequences {Xn} of E valued random variables such that (a) for each x* ε E*, x*(Xn) → 0 a.s. and yet (b) Xn does not go to zero weakly a.s.

Supported in part by NSF-MCS-74-07509.

Supported in part by NSF-MCS-72-04634.

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

References

  1. R. V. Chacon and L. Sucheston, On convergence of vector valued asymptotic martingales, Z. Warsch. 33 (1975), 55–59.

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Chatterji, Martingale convergence and the Radon-Nikodym theorem, Math. Scand. 22 (1968), 21–41.

    MathSciNet  MATH  Google Scholar 

  3. R. C. James, A separable somewhat reflexive space with nonseparable dual, B.A. M.S., 80 (1974), 738–743.

    Article  MathSciNet  MATH  Google Scholar 

  4. C. Stegall, The Radon-Nikodym property in conjugate Banach spaces," T.A.M.S., 20 (1975), 213–223.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Ohio State University, 43210, Columbus, OH, USA

    W. J. Davis & W. B. Johnson

Authors
  1. W. J. Davis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. B. Johnson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

J. Baker C. Cleaver J. Diestel

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Springer-Verlag

About this paper

Cite this paper

Davis, W.J., Johnson, W.B. (1977). Weakly convergent sequences of Banach space valued random variables. In: Baker, J., Cleaver, C., Diestel, J. (eds) Banach Spaces of Analytic Functions. Lecture Notes in Mathematics, vol 604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069202

Download citation

  • DOI: https://doi.org/10.1007/BFb0069202

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08356-6

  • Online ISBN: 978-3-540-37262-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation