Israel Journal of Mathematics

, Volume 37, Issue 1–2, pp 54–75 | Cite as

Martingales valued in certain subspaces ofL 1

  • J. Bourgain
  • H. P. Rosenthal


A Banach subspaceE ofL 1 is constructed such thatE fails the Radon-Nikodym property, yetE has no bounded dyadicδ-tree for anyδ>0. The unit ball ofE is also relatively compact in the topology of convergence in probability, which implies thatE has the strong Schur property. The construction uses martingales and probabilistic techniques.


Unit Ball Independent Random Variable Difference Sequence Borel Subset Finite Dimensional Subspace 
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Copyright information

© The Weizmann Science Press of Israel 1980

Authors and Affiliations

  • J. Bourgain
    • 1
    • 2
    • 3
  • H. P. Rosenthal
    • 1
    • 2
    • 3
  1. 1.University of Paris VIFrance
  2. 2.Free University of BrusselsBelgium
  3. 3.The University of Texas at AustinUSA

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