Quantitative differentiation: A general formulation

Research output: Contribution to journalArticle


Let dx denote Lebesgue measure on ℝ n. With respect to the measure C = r -1 dr × dx on the collection of balls B r(x) ⊂ ℝ n, the subcollection of balls B r(x) ⊂ B 1(0) has infinite measure. Let f: B 1(0) → ℝ have bounded gradient, |∇f

Original languageEnglish (US)
Pages (from-to)1641-1670
Number of pages30
JournalCommunications on Pure and Applied Mathematics
Issue number12
StatePublished - Dec 1 2012


ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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