Does almost everywhere differentiablty imply existence of weak derivitive? What about the converse? If not in general maybe on compacts?
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No, the Cantor function is a counterexample (differentiable almost everywhere, but not absolutely continuous). – Hans Engler Aug 03 '15 at 07:29
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@HansEngler ah, is abs. cts. the weakest that gives partial integration? I only need partial integration to hold a.e in order to get the definition of weak derivite right? – user123124 Aug 03 '15 at 07:33
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you're right of course. – Hans Engler Aug 04 '15 at 09:22
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Hans counterexample and this question Weakest hypothesis for integration by parts gives a clear picture of the situation
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