An elementary proof of the one-dimensional Rademacher theorem
Luděk Zajíček (1992)
Mathematica Bohemica
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An elementary short proof of the one-dimensional Rademacher theorem on differentiability of Lipschitz functions is given.
Displaying similar documents to “A simple proof of the Rademacher theorem”
An elementary proof of the one-dimensional Rademacher theorem
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Bi-Lipschitz trivialization of the distance function to a stratum of a stratification
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Given a Lipschitz stratification 𝒳 that additionally satisfies condition (δ) of Bekka-Trotman (for instance any Lipschitz stratification of a subanalytic set), we show that for every stratum N of 𝒳 the distance function to N is locally bi-Lipschitz trivial along N. The trivialization is obtained by integration of a Lipschitz vector field.
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It is shown that every bi-Lipschitz bijection from Z to itself is at a bounded L1 distance from either the identity or the reflection.We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.
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