# Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces

Analysis and Geometry in Metric Spaces (2015)

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

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topGuy 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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