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I have the following question: If A $A$ is a metrically oriented n-dimensional $n$-dimensional subset of \bR^N $\mathbb{R}^N$ and f $f$ is a continuous map from A $A$ to \bR^M. $\mathbb{R}^M$ . We know that Lip $\mathrm{Lip} f <\infty L^n-almost < +\infty$ $L^N$-almost everywhere, can we then continuously extends f to the whole \bR^N $\mathbb{R}^N$ such that Lip $\mathrm{Lip} f <\infty L^N-almost < +\infty$ $L^N$-almost everywhere? Here Lip f $\mathrm{Lip}$ is the local lipschitz constant of f.$f$.

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I have the following question: If A is a metrically oriented n-dimensional subset of \bR^N (n and f is a continuous map from A to \bR^M. We know that Lip f<\infty L^n-almost everywhere, can we then continuously extends f to the whole \bR^N such that Lip f<\infty L^N-almost everywhere? Here Lip f is the local lipschitz constant of f.

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# Can we extend a a.e. Lipschitz map defined on a closed subset of \bR^N to the whole space such that it is still a.e. Lipschitz

I have the following question: If A is a metrically oriented n-dimensional subset of \bR^N (n