Lopes Filho, Milton C.; Nussenzveig Lopes, Helena J. Pointwise blow-up of sequences bounded in \(L^1\). (English) Zbl 1030.46031 J. Math. Anal. Appl. 263, No. 2, 447-454 (2001). 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. Reviewer: Khalifa Trimèche (Tunis) Cited in 3 Documents 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 Keywords:integrable functions; Cantor sets; Hausdorff dimension PDFBibTeX XMLCite \textit{M. C. Lopes Filho} and \textit{H. J. Nussenzveig Lopes}, J. Math. Anal. Appl. 263, No. 2, 447--454 (2001; Zbl 1030.46031) Full Text: DOI References: [1] Billingsley, P., Probability and Measure (1986), Wiley: Wiley New York · Zbl 0649.60001 [2] Delort, J.-M., Existence de nappes de tourbillon en dimension deux, J. Amer. Math. Soc., 4, 553-586 (1991) · Zbl 0780.35073 [3] Falconer, K., Fractal Geometry: Mathematical Foundations and Applications (1990), Wiley: Wiley Chichester · Zbl 0689.28003 [4] Lopes Filho, M. C.; Nussenzveig Lopes, H. J.; Xin, Z., Existence of vortex sheets with reflection symmetry in two space dimensions, Arch. Rat. Mech. Anal., 158, 235-257 (2001) · Zbl 1058.35176 [5] Royden, H. L., Real Analysis (1968), Macmillan: Macmillan New York · Zbl 0197.03501 [6] Rudin, W., Real and Complex Analysis (1974), Tata McGraw-Hill: Tata McGraw-Hill New Delhi [7] Schochet, S., The weak vorticity formulation of the 2D Euler equations and concentration-cancellation, Comm. Partial Differential Equations, 20, 1077-1104 (1995) · Zbl 0822.35111 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.