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On convex total bounded sets in the space of measurable functions. (English) Zbl 1242.46037
Summary: We estimate the measure of nonconvex total boundedness in terms of simpler quantitative characteristics in the space of measurable functions \(L_0\). A Fréchet-Smulian type compactness criterion for convexly totally bounded subsets of \(L_0\) is established.
MSC:
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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