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
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