[FOM] Q and A
Kreinovich, Vladik
vladik at utep.edu
Wed Nov 7 16:42:41 EST 2007
If I remember correctly, in the sense of, e.g., the Wiener measure,
almost all continuous functions are not differentiable anywhere.
The major difference is that in Baire-category terms, you have absolute
results, but in measure-theoretic terms, you have to specify the
measure. For example, here are other measures on the set of all
continuous functions in terms of which almost all continuous functions
are differentiable.
> From joeshipman at aol.com
>> From: Gabriel Stolzenberg <gstolzen at math.bu.edu>
>> the set of continuous functions on [0,1] that are differentiable at
>> at least one point is a countable union of nowhere dense sets.
> Is there a measure-theoretic version of this or does it only work for
> category?
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