A Simple Proof of the Johnson–Lindenstrauss Extension Theorem

Abstract

Johnson and Lindenstrauss proved that any Lipschitz mapping from an n-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( log n). We present a simplification of their argument that avoids dimension reduction and the Kirszbraun theorem.

Locations

• American Mathematical Monthly - View
• arXiv (Cornell University) - View - PDF