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Kirszbraun theorem

In mathematics, the Kirszbraun theorem in mathematical analysis states that if U is a subset of Euclidean space En and

f : U → Em

is a Lipschitz-continuous map, then there is a Lipschitz-continuous map

F: En → Em

that extends f, and has the same Lipschitz constant as f.

Reference

M. D. Kirszbraun. Uber die zusammenziehenden und Lipschitzchen Transformationen. Fund. Math., (22):77–108, 1934.

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10-26-2009 08:16:03
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