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A Simple proof of Johnson-Lindenstrauss extension theorem

Abstract

Johnson and Lindenstrauss proved that any Lipschitz mapping from an nn-point subset of a metric space into Hilbert space can be extended to the whole space, while increasing the Lipschitz constant by a factor of O(logn)O(\sqrt{\log n}). We present a simplification of their argument that avoids dimension reduction and the Kirszbraun theorem.Comment: 3 pages. Incorporation of reviewers' suggestion

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