Geodesic
Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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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.
Mots-clés : Lipschitz, Lusin, PI space, Poincaré inequality, measurable differentiable structure 
@article{AGMS_2015_3_1_a16,
     author = {David, Guy C. David},
     title = {Lusin-type {Theorems} for {Cheeger} {Derivatives} on {Metric} {Measure} {Spaces}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2015},
     volume = {3},
     number = {1},
     zbl = {1325.26030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a16/}
}
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David, Guy C. David. Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a16/