I am an outsider for this field of mathematical analysis. But to analyse a problem of Control Systems, which is my area of interest, I need to know this.

I learned that *absolutely continuous functions* are also *differentiable almost everywhere*. On the other hand, *Lipschitz continuity* ensures *bounded derivative* of the function a.e. I am wondering whether there is any link between the derivative being bounded and the function being absolutely continuous. Or, is there any sufficient condition to be imposed over the *absolute continuity* to ascertain that the derivative of the function will be bounded?