A new proof of Fréchet differentiability of Lipschitz functions
Journal of the European Mathematical Society, Tome 2 (2000) no. 3, pp. 199-216
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Abstract. We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on Ê2 (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the w* closure of the set of its points of Gâteaux differentiability is norm separable.
@article{JEMS_2000_2_3_a0,
author = {Joram Lindenstrauss and David Preiss},
title = {A new proof of {Fr\'echet} differentiability of {Lipschitz} functions},
journal = {Journal of the European Mathematical Society},
pages = {199--216},
publisher = {mathdoc},
volume = {2},
number = {3},
year = {2000},
doi = {10.1007/s100970000019},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970000019/}
}
TY - JOUR AU - Joram Lindenstrauss AU - David Preiss TI - A new proof of Fréchet differentiability of Lipschitz functions JO - Journal of the European Mathematical Society PY - 2000 SP - 199 EP - 216 VL - 2 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1007/s100970000019/ DO - 10.1007/s100970000019 ID - JEMS_2000_2_3_a0 ER -
%0 Journal Article %A Joram Lindenstrauss %A David Preiss %T A new proof of Fréchet differentiability of Lipschitz functions %J Journal of the European Mathematical Society %D 2000 %P 199-216 %V 2 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1007/s100970000019/ %R 10.1007/s100970000019 %F JEMS_2000_2_3_a0
Joram Lindenstrauss; David Preiss. A new proof of Fréchet differentiability of Lipschitz functions. Journal of the European Mathematical Society, Tome 2 (2000) no. 3, pp. 199-216. doi: 10.1007/s100970000019
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