Norms supporting the Lebesgue differentiation theorem
Functional Analysis
2017-02-07 v1
Abstract
A version of the Lebesgue differentiation theorem is offered, where the norm is replaced with any rearrangement-invariant norm. Necessary and sufficient conditions for a norm of this kind to support the Lebesgue differentiation theorem are established. In particular, Lorentz, Orlicz and other customary norms for which Lebesgue's theorem holds are characterized.
Cite
@article{arxiv.1512.03202,
title = {Norms supporting the Lebesgue differentiation theorem},
author = {Paola Cavaliere and Andrea Cianchi and Luboš Pick and Lenka Slavíková},
journal= {arXiv preprint arXiv:1512.03202},
year = {2017}
}