Dubon, Eric, San Antolín Gil, Ángel
The Lebesgue differentiation theorem revisited
Expositiones Mathematicae. 2019, 37(3): 322-332. doi:10.1016/j.exmath.2019.02.001
URI: http://hdl.handle.net/10045/92488
DOI: 10.1016/j.exmath.2019.02.001
ISSN: 0723-0869 (Print)
Abstract: 
We prove a general version of the Lebesgue differentiation theorem where the averages are taken on a family of sets that may not shrink nicely to any point. These families of sets involve the unit ball and its dilated by negative integers of an expansive linear map. We also give a characterization of the Lebesgue measurable functions on R^n in terms of approximate continuity associated to an expansive linear map.
Keywords:A-approximate continuity, A-density point, Expansive linear maps, Lebesgue measurable functions, Lebesgue differentiation theorem
Elsevier
info:eu-repo/semantics/article