This function is Hölder continuous but not   Lipschitz continuous at all points, and is considered one of the monsters of real analysis.
This function is de ned in general by a sum of elements of the formsin(πka x) This function's graph has a Hausdor  dimension of 2 + ln a , where a and b are  lnbparameters used to de ne it, 0 &lt; a &lt; 1, and b is a positive odd integer greaterthan or equal to 7. This function is Hölder continuous but not   Lipschitz continuous at all points, and is considered one of the monsters of real analysis. This function is only di erentiable at a rational number if it is expressible as the ratio of two odd numbers. For ten points, identify this pathological func- tion which is continuous everywhere but di erentiable on a set with Lebesgue measure zero.
This function is de ned in general by a sum of elements of the formsin(πka x)
Weierstrass function