Strict monotonicity, lower local uniform monotonicity, upper local uniform monotonicity and their orthogonal counterparts are considered in the case of Musielak–Orlicz function spaces \(L^\Phi (\mu )\) endowed with the Mazur–Orlicz F-norm as well as in the case of their subspaces \(E^\Phi (\mu )\) with the F-norm induced from \(L^\Phi (\mu )\). The presented results generalize some of the results from Cui et al. (Aequ Math 93:311–343, 2019) and Hudzik et al. (J Nonlinear Convex Anal 17(10):1985–2011, 2016), obtained only for Orlicz spaces as well as their subspaces of order continuous elements equipped with the Mazur–Orlicz F-norm.

在赋予Mazur-Orlicz F-范数的Musielak-Orlicz函数空间\（L ^ \ Phi（\ mu）\）的情况下，考虑严格的单调性，较低的局部均匀单调性，较高的局部均匀单调性及其正交对应项就像它们的子空间\（E ^ \ Phi（\ mu）\）一样，具有从\（L ^ \ Phi（\ mu）\）引起的F范数。给出的结果概括了Cui等人的一些结果。（Aequ Math 93：311–343，2019）和Hudzik等人。（J非线性凸面分析17（10）：1985–2011，2016），仅针对Orlicz空间及其配备了Mazur-Orlicz F-范数的有序连续元素的子空间获得。