Geodesic
On Possible Values of Upper and Lower Derivatives with Respect to Convex Differential Bases
Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 762-775

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It is proved that if a convex density-like differential basis $B$ is centered and invariant with respect to translations and homotheties, then the integral means of a nonnegative integrable function with respect to $B$ can boundedly diverge only on a set of measure zero (this generalizes a theorem of Guzmán and Menarguez); it is established that both translation and homothety invariances are necessary. 
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     author = {G. G. Oniani},
     title = {On {Possible} {Values} of {Upper} and {Lower} {Derivatives} with {Respect} to {Convex} {Differential} {Bases}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {76},
     number = {5},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a11/}
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G. G. Oniani. On Possible Values of Upper and Lower Derivatives with Respect to Convex Differential Bases. Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 762-775. http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a11/