Points of monotonicity in Musielak-Orlicz function spaces endowed with the Luxemburg norm

Abstract

Points of lower monotonicity, upper monotonicity, lower local uniform monotonicity and upper local uniform monotonicity of Musielak-Orlicz spaces L M and of their subspaces E M of order continuous elements from L M are characterized in the case of a nonatomic measure space $ (G, \Sigma, \mu) $ if L M and E M are endowed with the Luxemburg norm. Criteria for strict monotonicity, lower local uniform monotonicity and upper local uniform monotonicity are easily deduced.