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.
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