Gateaux differentiable functions are somewhere Fréchet differentiable (Q1063206)

Let G be a nonempty open subset of an Asplund space (i.e. such real Banach space, all of whose separable subspaces have a separable dual) and let \(f: G\to {\mathbb{R}}\) be locally Lipschitz and Gâteaux differentiable at every point of G. Then the author has proved that f is Fréchet differentiable at uncountably many points of G. The nonseparable case is reduced to the separable one with the help of a general separable reduction theorem.