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.