[FOM] Category and Measure
Timothy Y. Chow
tchow at alum.mit.edu
Tue Sep 18 14:49:08 EDT 2007
Joe Shipman wrote:
> But, can someone explain what's so useful about meager sets when
> working with a measure space like the real numbers?
The pointwise limit of a sequence of continuous functions is continuous
except on a set of first category. So for example if f is everywhere
differentiable, then its derivative f' is continuous except on a set of
first category. I don't think there is a way to say the "same thing"
using measure.
Tim
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