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On the Orlicz space generated from a random normed module

arXiv: Functional Analysis(2015)

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Abstract
In this paper, we first introduce the notion of the Orlicz space generated from a random normed module $E$. Then we give a representation theorem which identify the dual of the Orlicz heart of $E$ with the Orlicz space generated from the random conjugate space of $E$. Finally, we establish relations between the strict convexity and uniform convexity of this Orlicz space and the random strict convexity and random uniform convexity of the underlying random normed module, respectively.
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