SOME BASIC RESULTS ON THE ORLICZ SPACE GENERATED FROM A RANDOM NORMED MODULE

Considering the important role played by the abstract L-P space in the development of random normed modules, in this paper we introduce and study the Orlicz space generated from a random normed module. First, we give a basic dual representation theorem which identifies the dual of the Orlicz heart of a random normed module with the Orlicz space generated from the random conjugate space. Then, we establish the respective equivalence relations between the strict convexity and uniform convexity of this abstract Orlicz space and the random strict convexity and random uniform convexity of the underlying random normed module. These results are quite general. If we appropriately choose the random normed module or the Orlicz function, our results reduce to some known results in the literature.