Geodesic
Dependence of differential properties of a~function on the speed of its rational approximations in the metrics of $L_p$
Matematičeskie zametki, Tome 15 (1974) no. 1, pp. 79-90

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We establish the existence almost everywhere on $[0,1]$ of a generalized differential of a given order for a function which can be sufficiently well approximated by rational functions in the metrics of $L_p[0,1]$ ($0$); we will clearly express the metric dimension of the set of points at which the function is not differentiable. 
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     author = {E. A. Sevast'yanov},
     title = {Dependence of differential properties of a~function on the speed of its rational approximations in the metrics of $L_p$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {79--90},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_1_a8/}
}
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E. A. Sevast'yanov. Dependence of differential properties of a~function on the speed of its rational approximations in the metrics of $L_p$. Matematičeskie zametki, Tome 15 (1974) no. 1, pp. 79-90. http://geodesic.mathdoc.fr/item/MZM_1974_15_1_a8/