A rough differentiable function - Kirchheim, B; Mueller, P (2008)
A real-valued continuously differentiable function f on the unit interval is constructed such that Γk=1∞ βf(x,2-k)=∞ holds for every x ∈ [0, 1]. Here βf(x, 2-k) measures the distance of f to the best approximating linear function at scale 2-k around x. © 2008 by the authors.