Embedding proper ultrametric spaces into ${\ell }_p$ and its application to nonlinear Dvoretzky's theorem

Abstract

We prove that every proper ultrametric space isometrically embeds into ${\ell }_p$ for any $p\ge 1$. As an application we discuss an ${\ell }_p$-version of nonlinear Dvoretzky's theorem.

6 pages

References in corpus (2)

• On some low distortion metric Ramsey problems
• Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theorem

Cited by in corpus (1)

• An embedding, an extension, and an interpolation of ultrametrics