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May 26, 2023 at 5:26 comment added Nate River Along the same lines, the Wiener measure gives positive measure to any open ball in $C[0, 1]$ (see here), and is fully supported on the set of continuous nowhere differentiable functions. This proves the density of nowhere differentiable functions in $C[0, 1]$.
S Mar 24, 2023 at 15:23 history answered John Dawkins CC BY-SA 4.0
S Mar 24, 2023 at 15:23 history made wiki Post Made Community Wiki by John Dawkins