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Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces

100%

David G. C. D.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

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.

Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation

100%

Cheeger J., Kleiner B., Schioppa A.

Analysis and Geometry in Metric Spaces

2016

tom 4

nr 1

We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14, 27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [27] is equal to 1, and new nonembeddability results.

Ograniczanie wyników

2 Analysis and Geometry in Metric Spaces

1 Cheeger J.

1 David G. C. D.

1 Kleiner B.

1 Schioppa A.

1 2016

1 2015

Wyniki wyszukiwania

Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces

Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation