Geometriae Dedicata

, Volume 172, Issue 1, pp 387–398 | Cite as

A doubling subset of \(L_p\) for \(p>2\) that is inherently infinite dimensional

  • Vincent Lafforgue
  • Assaf NaorEmail author
Original Paper


It is shown that for every \(p\in (2,\infty )\) there exists a doubling subset of \(L_p\) that does not admit a bi-Lipschitz embedding into \(\mathbb R^k\) for any \(k\in \mathbb N\).


Metric embeddings Heisenberg group Doubling metric spaces 

Mathematics Subject Classification

30L05 20F65 46E30 



V. L. was supported by ANR Grant KInd. A. N. was supported by NSF Grant CCF-0832795, BSF Grant 2010021, the Packard Foundation and the Simons Foundation. Part of this work was completed while A. N. was a Visiting Fellow at Princeton University.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques—Analyse, Probabilités, Modélisation—Orléans (MAPMO) UMR CNRS 6628Université d’Orléans Rue de ChartresOrléans cedex 2France
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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