chapter  22
Nondifferentiable functions from the point of view of category and measure
ByGilbert W. Bassett Jr., Roger Koenker
Pages 26

In some preceding sections of this book we were concerned with various continuous but nondifferentiable functions acting from R into R (see, e.g., Chapters 0 and 7). In the present chapter, we wish to discuss one general approach to such functions from the viewpoint of category and measure. Briefly speaking, our goal is to demonstrate that, for a given generalized notion of derivative (introduced within ZF & DC $ \mathbf{ZF}~ \& ~\mathbf{DC} $ theory), the set of real-valued continuous nondifferentiable functions (with respect to this notion) turns out to be sufficiently large.