From: Ronald Bruck Subject: Re: Frechet differentiability of Lipschitz functions Date: Mon, 22 Jan 2001 11:30:30 -0800 Newsgroups: sci.math.research Summary: Rademacher's theorem: Lipschitz implies differentiable a.e. In article <94fl45$cbs$1@agate.berkeley.edu>, chernoff@math.berkeley.edu (Paul R. Chernoff) wrote: :Suppose that f(x,y) is a real-valued Lipschitz function of two real :variables :(defined on the open unit square, say). Must f be Frechet differentiable :almost everywhere with respect to planar Lebesgue measure? : :(The corresponding result for functions of 1 real variable is an easy :consequence of Lebesgue's differentiation theorem.) : :Note: I would expect that this question has long since been investigated. It's known as Rademacher's Theorem, according to Frank Clarke's book ("Optimization and Nonsmooth Analysis"). And of course it's proved in R^N, not just R^2. --Ron Bruck -- Due to University fiscal constraints, .sigs may not be exceed one line.