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Proceedings of the American Mathematical Society

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

 

 

$ L\sb{p}(\mu ,X)$ $ (1<p<\infty )$ has the Radon-Nikodým property if $ X$ does by martingales


Authors: Barry Turett and J. J. Uhl
Journal: Proc. Amer. Math. Soc. 61 (1976), 347-350
MSC: Primary 46E40; Secondary 28A45
MathSciNet review: 0423069
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0423069-3
Article copyright: © Copyright 1976 American Mathematical Society