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The asymptotic norming property and martingale convergence

Author: D. van Dulst
Journal: Proc. Amer. Math. Soc. 89 (1983), 430-432
MSC: Primary 46B22; Secondary 60B11, 60G42
MathSciNet review: 715860
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Abstract: A martingale proof is given of the result of R. G. James and A. Ho in [3] that the asymptotic norming property implies the Radon-Nikodym property.

References [Enhancements On Off] (What's this?)

  • [1] S. D. Chatterji, Martingale convergence and the Radon-Nikodym theorem in Banach spaces, Math. Scand. 22 (1968), 21-41. MR 0246341 (39:7645)
  • [2] J. Diestel and J. J. Uhl, Jr., Vector measures, Math. Surveys, no. 15, Amer. Math. Soc, Providence, R. I., 1977. MR 0453964 (56:12216)
  • [3] R. C. James and Aggie Ho, The asymptotic-norming and Radon-Nikodym properties for Banach spaces, Ark. Mat. 19 (1981), 53-70. MR 625537 (82i:46033)
  • [4] P. McCartney and R. O'Brien, A separable Banach space with the Radon-Nikodym property which is not isomorphic to a subspace of a separable dual, Proc. Amer. Math. Soc. 78 (1980), 40-42. MR 548080 (81m:46035)
  • [5] J. Neveu, Discrete-parameter martingales, North-Holland, Amsterdam, 1975. MR 0402915 (53:6729)

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Article copyright: © Copyright 1983 American Mathematical Society

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