Geodesic
On the relationship between differentiability conditions and existence of a strong gradient
Matematičeskie zametki, Tome 77 (2005) no. 1, pp. 93-98.

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It is proved that for any $n\geqslant2$ there exists continuous function $f\colon\mathbb R^n\to\mathbb R$ which is differentiable almost everywhere, but has no strong gradient almost everywhere. 
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G. G. Oniani. On the relationship between differentiability conditions and existence of a strong gradient. Matematičeskie zametki, Tome 77 (2005) no. 1, pp. 93-98. http://geodesic.mathdoc.fr/item/MZM_2005_77_1_a7/

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[3] Saks S., Teoriya integrala, M., 1949 | Zbl