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arXiv · 2501.00853

A dual representation theorem on the conditional Orlicz space generated from a random normed module

Xia Zhang·Ke Qian·Ming Liu
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Abstract

In this paper, we first introduce the notion of a random Orlicz function, and further present the conditional Orlicz space generated from a random normed module. Second, we prove the denseness of the Orlicz heart of a random normed module $E$ in $E$ with respect to the $(\varepsilon, \lambda)$-topology. Finally, based on the above work, we establish a dual representation theorem on the conditional Orlicz space generated from a random normed module, which extends and improves some known results.

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Xia Zhang, Ke Qian, Ming Liu. 2025-01-01. A dual representation theorem on the conditional Orlicz space generated from a random normed module. https://arxiv.org/abs/2501.00853

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