[Sur la propriété d'extension lipschitzienne absolue]
On dit qu'un espace métrique X a la propriété d'extension lipschitzienne absolue si pour tout espace de Banach Z, toute fonction lipschitzienne f de X dans Z peut être étendue à tout espace métrique Y contenant X, avec une perte dans la constante de Lipschitz de l'extension qui ne dépend pas du choix de Y,Z et f. Nous montrons que plusieurs classes naturelles d'espaces métriques ont la propriété d'extension lipschitzienne absolue.
A metric space X is said to be absolutely Lipschitz extendable if every Lipschitz function f from X into any Banach space Z can be extended to any containing space Y⊇X, where the loss in the Lipschitz constant in the extension is independent of , and f. We show that various classes of natural metric spaces are absolutely Lipschitz extendable.
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@article{CRMATH_2004__338_11_859_0,
author = {Lee, James R. and Naor, Assar},
title = {Absolute {Lipschitz} extendability},
journal = {Comptes Rendus. Math\'ematique},
pages = {859--862},
publisher = {Elsevier},
volume = {338},
number = {11},
year = {2004},
doi = {10.1016/j.crma.2004.03.005},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.03.005/}
}
TY - JOUR AU - Lee, James R. AU - Naor, Assar TI - Absolute Lipschitz extendability JO - Comptes Rendus. Mathématique PY - 2004 SP - 859 EP - 862 VL - 338 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.03.005/ DO - 10.1016/j.crma.2004.03.005 LA - en ID - CRMATH_2004__338_11_859_0 ER -
Lee, James R.; Naor, Assar. Absolute Lipschitz extendability. Comptes Rendus. Mathématique, Tome 338 (2004) no. 11, pp. 859-862. doi : 10.1016/j.crma.2004.03.005. http://www.numdam.org/articles/10.1016/j.crma.2004.03.005/
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