Talk:Kirszbraun theorem

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Is this really true? I think that the assumption that En be metrized with the L^\infty norm has been dropped! See the article from 1956 by Aronszajn and Panitchpakdi, "Extension of uniformly continuous mappings and hyperconvex spaces", Pacific Journal of Mathematics (I can't remember the volume number).

No it is ok, the metric is Euclidean Tosha 20:41, 8 Nov 2004 (UTC)

And where can I find the proof? mbork 09:00, 2004 Nov 15 (UTC)

There is a good extension of this result to metric spaces: If S is a subset of a metric space (X,d), and if f:S→R is K-Lipschitz, then f:X→R defined by

f(x):=sup{f(y)-Kd(x,y)|y∈S}

equals f on S and is K-Lipschitz. It is easy to check that f works. The result is from E. J. McShane, Extensions of Range of Functions, Bull. Am. Math. Soc., 40 1934, 837-842. It is interesting that these two papers were published in the same year. I don't know the history. -Craig Calcaterra