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Sequentially compact sets in a class of generalized Orlicz spaces. (English) Zbl 1090.46011
The author characterizes sequentially compact sets in a class of generalized Orlicz spaces $$L^ {(M^ {-1})}$$. Note that those are Orlicz type spaces generated by the inverse function $$M^ {-1}$$ to an Orlicz function $$M$$ (i.e., $$M$$ is even, continuous and convex on $$(0,\infty )$$ such that $$M(0)=0$$, $$M(u)>0$$ for all $$u\neq 0$$ and $$\lim _ {u\to 0}\frac {M(u)}u=0$$, $$\lim _ {u\to \infty }\frac {M(u)}u=\infty$$) satisfy the $$\Delta _ 2$$-condition.
Reviewer: Petr Gurka (Praha)
##### MSC:
 46B20 Geometry and structure of normed linear spaces 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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