On the latticity of projection and antiprojection sets in Orlicz-Musielak spaces

We discuss the latticial structure of projection sets and antiprojection sets in Orlicz-Musielak spaces L ^Φ, with the distance given by modular ρ _Φ and classical F-norms generated by ρ _Φ. In particular, we show that the case of Amemiya F-norm is essentially different from others. This extends results given for sets of best approximants by Landers and Rogge, Kilmer and Kozlowski, and Mazzone.