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Pointwise blow-up of sequences bounded in \(L^1\). (English) Zbl 1030.46031

Given a sequence of functions bounded in \(L^1([0,1])\), is it possible to extract a subsequence that is pointwise bounded almost everywhere? In this paper the authors present an example showing that this not possible in general and prove a pair of positive results.

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
28A78 Hausdorff and packing measures
28A80 Fractals
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