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A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.

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Optimality of p-Lebesgue Differentiation Theorem for Sobolev Functions

It depends on the values of $p$ and $N$ - sometimes there will be counterexamples and sometimes there will not. For instance, any function $f \in W^{1,q}$ for $q>N$ is classically differentiable almo …
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