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Gateaux differentiable functions are somewhere Frechet differentiable

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Abstract

It is proved that every everywhere Gateaux differentiable real-valued Lipschitz function on an Asplund space is Frechet differentiable at uncountably many points. The nonseparable case is reduced to the separable one with the help of a general separable reduction theorem.

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Authors and Affiliations

  1. Faculty of Mathematies and Physics, Charles University, Sokolovska 83, 18600, Praha 8, Czechoslovakia

    David Preiss

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  1. David Preiss
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Additional information

Part of this work was made in the framework of activities of D. Preiss as visiting professor at University of Palermo sponsored by C.N.R. of Italy. The hospitality of the Circolo Matematico di Palermo is also gratefully acknowledged.

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Preiss, D. Gateaux differentiable functions are somewhere Frechet differentiable. Rend. Circ. Mat. Palermo 33, 122–133 (1984). https://doi.org/10.1007/BF02844417

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  • DOI: https://doi.org/10.1007/BF02844417

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