[FOM] Category and Measure

[Timothy Y. Chow]

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