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Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces

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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.
Opis fizyczny
  • Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012
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