Editing Absolute continuity (section)

===Examples===
The following functions are uniformly continuous but '''not''' absolutely continuous:
* The [[Cantor function]] on [0, 1] (it is of bounded variation but not absolutely continuous);
* The function:<math display="block"> f(x) = \begin{cases}
0, & \text{if }x =0 \\
x \sin(1/x), & \text{if } x \neq 0
\end{cases} </math> on a finite interval containing the origin.

The following functions are absolutely continuous but not α-Hölder continuous:
* The function ''f''(''x'')&nbsp;=&nbsp;''x<sup>β</sup>'' on [0,&nbsp;''c''], for any {{nowrap|0 < ''β'' < ''α'' < 1}}

The following functions are absolutely continuous and [[Hölder condition|α-Hölder continuous]] but not [[Lipschitz continuity|Lipschitz continuous]]:
* The function ''f''(''x'')&nbsp;=&nbsp;{{radic|''x''}} on [0,&nbsp;''c''], for ''α''&nbsp;≤&nbsp;1/2.