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.
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