Lusin-type theorems for Cheeger derivatives on metric measure spaces

2015/02/03 by Guy C. David, David, Guy C.
Mathematics · #26B05 #30L99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG) #math.CA #math.MG #msc:26B05 #msc:30L99

paper · pdf · doi:10.48550/arxiv.1502.00694

16 pages. Comments welcome

arxiv created 2015/02/03 · arxiv updated 2015/02/04

Abstract

A theorem of Lusin states that every Borel function on R is 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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