Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation

Jeff Cheeger, Bruce Kleiner, Andrea Schioppa

Research output: Contribution to journalArticlepeer-review


We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14, 27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [27] is equal to 1, and new nonembeddability results.

Original languageEnglish (US)
Pages (from-to)104-159
Number of pages56
JournalAnalysis and Geometry in Metric Spaces
Issue number1
StatePublished - 2016


  • Metric measure space
  • bi-Lipschitz embedding
  • differentiability space
  • measurable differentiable structure
  • metric differentiation

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Applied Mathematics


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