On the differentiability of norms in Banach spaces

The purpose of this paper is to show some particularities that the differentiability sets generated from the norms have in the Banach spaces. In this sense, it will be shown that the Gaussian measure of the Frechet differentiability set of the norm of the space l(infinity) (R) of real bounded sequences is zero and that in the case of the space BV [a, b] of bounded variation functions its norm is not Frechet derivable in any element of this space.