EXTREME-POINTS OF THE UNIT BALL OF THE SPACE OF LIPSHITZ FUNCTIONS

We consider the space of all Lipschitz functions on a metric space wit h bounded Lipschitz norm, and give an intrinsic characterization of th e extreme points of the unit ball. We briefly discuss some examples of extreme Lipschitz functions, and apply the result to show that if the norm of a Banach space is Gateaux differentiable then extreme functio ns on any one-dimensional subspace may be canonically extended to extr eme functions on the whole space.