Geodesic
Note on Besicovitch's Theorem on the Possible Values of Upper and Lower Derivatives
Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 246-251

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Let $B_1,\dots,B_k$ be Busemann–Feller and regular differential bases composed of intervals of the corresponding dimensions. It is proved that if $B_1,\dots,B_k$ satisfy a certain condition (called the completeness condition), then, for their Cartesian product $B_1\times \dotsb\times B_k$, an analog of Besicovitch's theorem on the possible values of strong upper and lower derivatives is valid.
Keywords: Besicovitch's theorem on the values of upper and lower derivatives, Busemann–Feller basis, regular differentiation basis. 
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     author = {G. G. Oniani},
     title = {Note on {Besicovitch's} {Theorem} on the {Possible} {Values} of {Upper} and {Lower} {Derivatives}},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a8/}
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G. G. Oniani. Note on Besicovitch's Theorem on the Possible Values of Upper and Lower Derivatives. Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 246-251. http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a8/