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Distributional derivative is locally integrable - then the distribution as well?Given a distribution $T \in D'(\mathbb{R})$ such that the distributional derivative $\partial T \in L^1_{loc}(\mathbb{R})$. Can one deduce that $T \in L^1_{loc}(\mathbb{R})$ as well? Or can anyone give me an example where $T \notin L^1_{loc}(\mathbb{R})$?
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