Abstract

In this paper we are concerned with the pointwise behaviour of functions in certain classes of weakly differentiable functions. The ancestor of all modern results dealing with pointwise properties of nonsmooth functions is certainly the Lebesgue differentiation theorem, which asserts that if ft is an open subset of R ~, n > l , and u is a locally integrable function in f~, then lim~_~0+ 3CB,.(x) u(y) dy exists and is finite for a.e. xEf~, and

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