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May 30, 2021 at 5:25 comment added Nagaraj Iyengar Given a bounded open set of R^n one can only stuff the interior with a countable number of cusp singularities.This follows from the Nikodym property of W^(1,p)(R^n)
Sep 15, 2011 at 3:06 comment added Ian Agol I used Rademacher's theorem once to define a generalization of conformal volume of orbifolds (defined by Li-Yau). The notion of conformal volume is well-defined for Lipschitz maps by Rademacher's theorem. This was useful to us, since we could estimate the conformal volume for certain Lipschitz maps (of course, they were actually piecewise smooth, but Liptschitz seemed to be the natural category of maps).
Sep 15, 2011 at 1:08 history answered Bill Johnson CC BY-SA 3.0