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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