Daneš theorem in complete random normed modules

Based on the recent work of random metric theory, namely the Ekeland variationalprinciple on a complete random metric space, this paper studies the Daneštheorem in a complete random normed module. In this paper, we first present thenotion of finer ordering on a random normed module. Then we establish the Daneštheorem in a complete random normed module under the locally L0-convex topology. When the base space of the randomnormed module is trivial, our result automatically degenerates to the classicalcase.