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

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.