6533b7cefe1ef96bd1257991

RESEARCH PRODUCT

POINTS OF $\varepsilon$ -DIFFERENTIABILITY OF LIPSCHITZ FUNCTIONS FROM ${\bb R}^n$ TO ${\bb R}^{n-1}$

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This paper proves that for every Lipschitz function $f:{\bb R}^n\longrightarrow {\bb R}^m,\;m < n$ , there exists at least one point of $\varepsilon$ -differentiability of $f$ which is in the union of all $m$ -dimensional affine subspaces of the form $q_0+{\rm span}\{q_1,q_2,\ldots,q_m\},\;{\rm where}\;q_j(j=0,1,\ldots,m)$ are points in ${\bb R}^n$ with rational coordinates.