Drop properties and approximative compactness in Orlicz–Bochner function spaces

The representation of dual spaces of EM(μ,X), owing to its extensive application, is given in this paper. Using the representation, we get the sufficient and necessary conditions of LM(μ,X) possessing drop property, and extend the result of Hudzik and Wang [H. Hudzik, B. Wang, Approximative compactness in Orlicz spaces, J. Approx. Theory 95 (1998) 82–89]. Simultaneously, under some conditions, the weak∗ drop property in LM(μ,X∗) and LM∗(μ,X) is discussed.