A generalization of an Ekeland-Lebourg theorem and the differentiability of distance functions

Zajíček, L.

Displaying similar documents to “A generalization of an Ekeland-Lebourg theorem and the differentiability of distance functions”

On the Fréchet differentiability of distance functions

Zajíček, L.

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Remarks on Fréchet differentiability of pointwise Lipschitz, cone-monotone and quasiconvex functions

Luděk Zajíček (2014)

Commentationes Mathematicae Universitatis Carolinae

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We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on $Γ$ -almost everywhere Fréchet differentiability of Lipschitz functions on $c_{0}$ (and similar Banach spaces). For example, in these spaces, every continuous real function is Fréchet differentiable at $Γ$ -almost every $x$ at which it is Gâteaux differentiable. Another interesting consequences say that both cone-monotone functions and continuous quasiconvex functions on these spaces are $Γ$ -almost everywhere Fréchet...