Charles University in Prague, Faculty of Mathematics and Physics
Abstract
summary:In this paper we give a characterization of σ-order continuity of modular function spaces Lϱ in terms of the existence of best approximants by elements of order closed sublattices of Lϱ. We consider separately the case of Musielak--Orlicz spaces generated by non-σ-finite measures. Such spaces are not modular function spaces and the proofs require somewhat different methods