It is well known that the Brownian motion is an example of functions that is continuous but nowhere differentiable. In addition, its distributional derivative can be interpreted in the way mentioned in this page.
So, how is the other functions? Can one consider the distributional derivative for functions like the Weierstrass function, Takagi function and so on? Also, am I correct in understanding that the distributional derivative of the brownian motion is a measure which is discontinuous?
Please tell me if you know.