Towards Nikishin’s theorem on the almost sure convergence of rearrangements of functional series

  • S. Levental
  • V. Mandrekar
  • S. A. Chobanyan


Necessary and sufficient conditions are found for the almost sure convergence of almost all simple rearrangements of a series of Banach space valued random variables. The results go back to Nikishin’s well-known theorem on the existence of an almost surely convergent rearrangement of a numerical random series. An example is also given of a numerical random series with general term tending to zero almost surely such that this series converges in probability and any its rearrangement diverges almost surely.

Key words

rearrangement of a series in a Banach space almost sure convergence k-simple permutation Nikishin’s theorem 


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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • S. Levental
    • 1
  • V. Mandrekar
    • 1
  • S. A. Chobanyan
    • 2
  1. 1.Michigan State UniversityEast Gull Lake DriveUSA
  2. 2.Muskhelishvili Institute of Computational MathematicsTbilisiUSA

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