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

Luděk Zajíček (2014)

Commentationes Mathematicae Universitatis Carolinae

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 differentiable....

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