Juha Kinnunen ( Pointwise behaviour of Sobolev functions on metric spaces)

Abstract. We study Lebesgue points for Sobolev functions on metric measure spaces over collections of sets called differentiation bases. Our main result gives several conditions for a differentiation basis which characterize the existence of Lebesgue points outside a set of capacity zero. An interesting feature is that a qualitative result, as the existence of Lebesgue points, is implies quantitative estimates.


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