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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 15, 2015

Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces

  • Guy C. David


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.


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Received: 2015-2-5
Accepted: 2015-9-15
Published Online: 2015-10-15

© 2015 Guy C. David

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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