On differentiability properties of typical continuous functions and Haar null sets
On differentiability properties of typical continuous functions and Haar null sets
Let $D$ ($D^*$) be the set of all continuous functions $f$ on $[0,1]$ which have a derivative $f’(x)\in \mathbf {R}$ ($f’(x)\in \mathbf {R}^*$, respectively) at least at one point $x \in (0,1)$. B. R. Hunt (1994) proved that $D$ is Haar null (in Christensen’s sense) in $C[0,1]$. In the present …