Page "Lipschitz continuity" Paragraph 32

* A Lipschitz function g: R → R is absolutely continuous and therefore is differentiable almost everywhere, that is, differentiable at every point outside a set of Lebesgue measure zero.

Its derivative is essentially bounded in magnitude by the Lipschitz constant, and for a < b, the difference g ( b ) − g ( a ) is equal to the integral of the derivative g ′ on the interval.