Lipschitz Continuous Functions: Differentiable Almost Everywhere?

[lavinia]

Someone told me that a continuous function that is Lipschitz is differentiable almost every where. If this is true how do I see it?

 

[VeeEight]

Think about the relationship between Lipschitz, Absolute Continuity, and Bounded Variation. Which implies the other? Do you know any lemma that states that an AC or BV function has derivative almost everywhere?