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- W2277062810 abstract "On complete metric spaces that support doubling measures, we show that the validity of a Rademacher theorem for Lipschitz functions can be characterised by Keith's Lip-lip condition. Roughly speaking, this means that at almost every point, the infinitesmal behavior of every Lipschitz function is essentially independent of the scales used in the blow-up at that point. Moreover, the doubling property can be further weakened to a local hypothesis on the measure; we also present results in this direction. Our techniques of proof are new and may be of independent interest. They include an explicit use of coordinate charts for measurable differentiable structures, as well as a blow-up procedure on Euclidean spaces that preserves Weaver derivations." @default.
- W2277062810 created "2016-06-24" @default.
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- W2277062810 date "2012-08-14" @default.
- W2277062810 modified "2023-09-27" @default.
- W2277062810 title "The Lip-lip condition on metric measure spaces" @default.
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