### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 1641-1670 |

Number of pages | 30 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 65 |

Issue number | 12 |

DOIs | |

State | Published - Dec 2012 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Quantitative differentiation : A general formulation.** / Cheeger, Jeff.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 65, no. 12, pp. 1641-1670. https://doi.org/10.1002/cpa.21424

}

TY - JOUR

T1 - Quantitative differentiation

T2 - A general formulation

AU - Cheeger, Jeff

PY - 2012/12

Y1 - 2012/12

N2 - 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

AB - 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

UR - http://www.scopus.com/inward/record.url?scp=84867615099&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867615099&partnerID=8YFLogxK

U2 - 10.1002/cpa.21424

DO - 10.1002/cpa.21424

M3 - Article

VL - 65

SP - 1641

EP - 1670

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 12

ER -