Talk:Carathéodory's existence theorem

Absolute continuity doesn't imply almost everywhere differentiability.

At the end of the introduction it says "The absolute continuity of y implies that its derivative exists almost everywhere.", which, as far as I understand is false, e.g. fractal curves like the Weierstrass function. Of course, in this context it doens't work because such a function cannot be the solution to a differential equation, but I was wondering if there exist any Lebesgue integrable nowhere-differentiable functions, that could be Caratheodory solutions? 186.30.50.188 (talk) 02:53, 27 September 2024 (UTC)