Let X be a separable Fréchet space. In this paper we define a class A of null sets in X that is properly contained in the class of Aronszajn null sets, and we prove that a Lipschitz map from an open subset of X into a Gelfand-Fréchet space is Gateaux differentiable outside a set belonging to A.
La Russa, C. (2010). Rademacher Theorem for Fréchet spaces. QUAESTIONES MATHEMATICAE, 33(3), 263-275.
Rademacher Theorem for Fréchet spaces
LA RUSSA, Caterina
2010-01-01
Abstract
Let X be a separable Fréchet space. In this paper we define a class A of null sets in X that is properly contained in the class of Aronszajn null sets, and we prove that a Lipschitz map from an open subset of X into a Gelfand-Fréchet space is Gateaux differentiable outside a set belonging to A.
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