Geodesic
On~an~estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions
Izvestiya. Mathematics , Tome 26 (1986) no. 2, pp. 347-369.

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This paper establishes best possible conditions, on the degree of approximation of functions $f(x_1,\dots,x_m)$ in $L_p([0,1]^m)$ ($0$) by rational functions, that guarantee that the function $f$ has a $p$th mean differential of order $\lambda>0$ everywhere except on a set of zero Hausdorff ($m-1+\alpha$) measure ($0\alpha\leqslant1$). Bibliography: 11 titles. 
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E. A. Sevast'yanov. On~an~estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions. Izvestiya. Mathematics , Tome 26 (1986) no. 2, pp. 347-369. http://geodesic.mathdoc.fr/item/IM2_1986_26_2_a5/

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[7] Sevastyanov E. A., “Kusochno-monotonnaya approksimatsiya i $\Phi$-variatsii”, Anal. Math., 1:2 (1975), 141–164 | DOI | MR

[8] Sevastyanov E. A., “Nekotorye otsenki proizvodnykh ratsionalnykh funktsii v integralnykh metrikakh”, Matem. zametki, 13:4 (1973), 499–510

[9] Gusman M., Differentsirovanie integralov v $\mathbf R^n$, Mir, M., 1978 | MR

[10] Dolzhenko E. P., “Nekotorye metricheskie svoistva algebraicheskikh giperpoverkhnostei”, Izv. AN SSSR. Ser. matem., 27:2 (1963), 241–252

[11] Rusak V. N., “Sopryazhennye ratsionalnye funktsii i otsenki ikh proizvodnykh”, Izv. AN BSSR, seriya fiz.-matem. nauk, 1969, no. 3, 26–33 | MR | Zbl