[EM] Strong FBC, at last
fsimmons at pcc.edu
Thu Jan 30 12:19:42 PST 2003
On Thu, 30 Jan 2003, Alex Small wrote:
> Well, what's the weakest condition we could impose to guarantee that the
> boundaries have normals? You've said that fractal boundaries don't
> necessarily have normals. Obviously boundaries specified by linear
> equations would have normals, except perhaps at kinks, but that's a more
> restrictive assumption than I want to impose.
There's no shame in just including local linearity or the existence of
normals as part of the hypothesis.
On the other hand, it would be nice to have it come out as a consequence
of some natural requirement that non-mathematicians could appreciate.
A monotone function can be non-differentiable only on a set of measure
zero, so perhaps monotonicity would be sufficient.
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