On an estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions

This paper establishes best possible conditions, on the degree of approximation of functions $f(x_1,…,x_m)$ in $L_p([0,1]^m)$ ($0<p\leqslant\infty$) 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 ($0<\alpha\leqslant1$).
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