Abstract
We show that although the differentiability and the weak differentiability are different “locally”, these notions coincide almost everywhere “globally”. It is proved that a Banach space valued function F : [0, 1] → X is differentiable almost everywhere on [0, 1], if and only if F is weakly differentiable almost everywhere on [0, 1].
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Kaliaj, S.B. Differentiability and Weak Differentiability. Mediterr. J. Math. 13, 2801–2811 (2016). https://doi.org/10.1007/s00009-015-0656-6
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DOI: https://doi.org/10.1007/s00009-015-0656-6