Valuations on Orlicz spaces and LϕLϕ-star sets

In A. Tsang (2010) [21], a representation theorem was established for continuous valuations on LpLp-spaces whose underlying measure is non-atomic. In this paper, we generalize the results of A. Tsang (2010) [21] to Orlicz spaces, LϕLϕ. We also show that the results of D. Klain (1997) [6] can be extended to LϕLϕ-star valuations.