There are two important types of differentiability for Lipschitz functions between infinite dimensional Banach spaces.For Gateaux differentiability of such functions there is a satisfactory general existence theorem.However,Gateaux are only weak linear approximations of a function.It is much more desirable to have points of Frechet differentiability.It turns out that it is very hard to prove the existence of such points.One source of the difficulty is to find a proper notion of "almost everywhere" In a joint recent work with David Preiss we introduced a new notion of null sets which enables to prove existence results for points of Frechet differentiability in some important special cases.