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Smoothness and approximative compactness in Orlicz function spaces. (English) Zbl 1370.46013
Summary: Some criteria for approximative compactness of every weakly$$^*$$ closed convex set of Orlicz function spaces equipped with the Luxemburg norm are given. Although, criteria for approximative compactness of Orlicz function spaces equipped with the Luxemburg norm were known, we can easily deduce them from our main results.

##### MSC:
 46B50 Compactness in Banach (or normed) spaces 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46B20 Geometry and structure of normed linear spaces
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