The Subdifferentiability Properties of Typical Functions in Cw0, 1x

Let C denote the Banach space of continuous real valued functions onw0, 1xwith the uniform norm; ­a and ­cf denote the approximate subdifferential and Clarke subdifferential. It is proved that there exists a residual set A;C such that for every fgA we have ­af x.sRs­cf x. for each xgw0, 1x. Moreover, every function fgA is nowhere subdifferentially regular in 0, 1..