As a quick guess, the Cantor staircase ought to have those properties.
Could you please help me find an example of the following:
a function which is uniformly continuous but not absolutely continuous.
Definitions:
Uniformly continuous: A function f is uniformly continuous if such that
Absolutely continuous: A function F is absolutely continuous on [a,b] if given so that whenever at intervals all disjoint.
As a quick guess, the Cantor staircase ought to have those properties.