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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$L_{p}(\mu ,X)$ $(1<p<\infty )$ has the Radon-Nikodým property if $X$ does by martingales
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by Barry Turett and J. J. Uhl PDF
Proc. Amer. Math. Soc. 61 (1976), 347-350 Request permission

Abstract:

Using the fact that ${L_p}[0,\;1]\;(1 < p < \infty )$ has an unconditional basis, Sundaresan has shown that ${L_p}(\mu ,\;X)$ has the Radon-Nikodým property if $1 < p < \infty$ and $X$ has the Radon-Nikodým property. In this note, Sundaresan’s theorem is proved by direct martingale methods. Then it is shown how to adapt this argument to the context of Orlicz spaces in which Sundaresan’s argument is not applicable.
References
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 61 (1976), 347-350
  • MSC: Primary 46E40; Secondary 28A45
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0423069-3
  • MathSciNet review: 0423069