Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces

Guy C. David

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 296-312, electronic only
  • ISSN: 2299-3274

Abstract

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A theorem of Lusin states that every Borel function onRis equal almost everywhere to the derivative of a continuous function. This result was later generalized to Rn in works of Alberti and Moonens-Pfeffer. In this note, we prove direct analogs of these results on a large class of metric measure spaces, those with doubling measures and Poincaré inequalities, which admit a form of differentiation by a famous theorem of Cheeger.

How to cite

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Guy C. David. "Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces." Analysis and Geometry in Metric Spaces 3.1 (2015): 296-312, electronic only. <http://eudml.org/doc/275916>.

@article{GuyC2015,
abstract = {A theorem of Lusin states that every Borel function onRis equal almost everywhere to the derivative of a continuous function. This result was later generalized to Rn in works of Alberti and Moonens-Pfeffer. In this note, we prove direct analogs of these results on a large class of metric measure spaces, those with doubling measures and Poincaré inequalities, which admit a form of differentiation by a famous theorem of Cheeger.},
author = {Guy C. David},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Lipschitz; Lusin; PI space; Poincaré inequality; measurable differentiable structure},
language = {eng},
number = {1},
pages = {296-312, electronic only},
title = {Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces},
url = {http://eudml.org/doc/275916},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Guy C. David
TI - Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 296
EP - 312, electronic only
AB - A theorem of Lusin states that every Borel function onRis equal almost everywhere to the derivative of a continuous function. This result was later generalized to Rn in works of Alberti and Moonens-Pfeffer. In this note, we prove direct analogs of these results on a large class of metric measure spaces, those with doubling measures and Poincaré inequalities, which admit a form of differentiation by a famous theorem of Cheeger.
LA - eng
KW - Lipschitz; Lusin; PI space; Poincaré inequality; measurable differentiable structure
UR - http://eudml.org/doc/275916
ER -

References

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